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Sum of logarithms with same base | Logarithms | Algebra II | Khan Academy

Video vocabulary

exponential

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US / ˌekspəˈnenʃl /

UK / ˌɛkspəˈnɛnʃəl /

C1
  • adjecitve
  • (Of an increase) at a faster and faster rate

logarithmic

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US / ˌlɒɡə'rɪðmɪk /

UK / ˌlɒɡə'rɪðmɪk /

A1
  • adjecitve
  • Concerning or using logarithms

make

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US / meɪk /

UK / mek /

A1
  • noun
  • Product made by a particular company; brand
  • verb
  • To arrange or prepare something e.g. dinner
  • To get to (a place) on time
  • To gain the status of (teacher, lawyer, etc.)
  • To create something by putting things together
  • To earn a certain amount of money at a job
  • To cause or force a person to do something
  • To cause something to happen or be formed

one

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US / wʌn /

UK / wʌn /

A1
  • pronoun
  • You; we; people in general; someone
  • The thing or person previously referred to
  • adjecitve
  • Used to refer to people generally
  • Being a strong example of (something mentioned)
  • number
  • Number 1

power

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US / 'paʊə(r) /

UK / ˈpaʊɚ /

A1
  • noun
  • Legal or official right to perform certain actions
  • Ability to move forcefully and quickly
  • Energy of something (e.g. electricity or fuel)
  • Mathematical way to multiply a number
  • Condition of being in political control
  • Physical force, energy, and strength
  • verb
  • To give energy to something, e.g. by electricity
  • To move something forcefully and quickly

than

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US / ðən /

UK / ðən /

A1
  • conjunction
  • Used to compare two things that are not equal

term

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US / tɜ:m /

UK / tɚm /

A1
  • noun
  • Conditions applying to an agreement, contract
  • Length of time something is expected to happen
  • Fixed period of weeks for learning at school
  • The (precise) name given to something
  • verb
  • To call; give a name to

this

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US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

how

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US / haʊ /

UK / haʊ /

A1
  • adjecitve
  • To what degree? in what amount?
  • adverb
  • (Used to explain the way to do something)
  • exclamation
  • For what purpose or reason?
  • (Used to ask someone or something's condition)

you

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US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

let

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US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

little

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US / 'lɪtl /

UK / ˈlɪtl /

A1
  • adjecitve
  • Being short in length of time
  • Not great in size, amount, or degree; small
  • Being very young or younger than others
  • adverb
  • By an amount or degree that is not very much
  • Not often; rarely
  • noun
  • A person's name

the

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US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

clear

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US / klɪə(r) /

UK / klɪr /

A1
  • adjecitve
  • Empty; without anything in it or on it
  • Being certain and without doubt
  • Being without any streaks, spots, or cracks
  • Easy to understand; well-explained; obvious
  • adverb
  • Completely; entirely; through the whole of
  • Away from; free from
  • verb
  • To recover from or remove a problem
  • To get rid of the entire contents of
  • To give permission for something to happen
  • To make a place or surface empty by removing
  • To prove that someone is not guilty or to blame

raise

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US / reɪz /

UK / rez /

A1
  • noun
  • Increase in a bet above another when playing cards
  • Pay increase
  • verb
  • To increase a bet above another when playing cards
  • To gather donations for a cause or charity
  • To bring up and educate a child to maturity
  • To bring a dead person to life
  • To increase a quantity, size, intensity or price
  • To lift (e.g. your hand) to a higher position
  • To mention a topic /issue for discussion; bring up
  • To increase (salary, etc.)
  • To grow or care for plants or animals

exponent

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US / ɪkˈspəʊnənt /

UK / ɪkˈsponənt, ˈɛkˌsponənt /

C1
  • noun
  • Person who exemplifies an art movement, etc.

could

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US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

know

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US / nəʊ /

UK / noʊ /

A1
  • verb
  • To be familiar with a person or place, thing
  • To feel sure or be convinced about something
  • To discover or be aware of something
  • To be able to distinguish
  • To have knowledge of things

have

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US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

part

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US / pɑ:t /

UK / pɑ:rt /

A1
  • adjecitve
  • To some degree; half; not fully
  • noun
  • Division of a book
  • Ratio of something, e.g. 3 of gin, 1 of tonic
  • A line in a person's hair, made with a comb
  • Character an actor plays on stage, movie, or TV
  • Some, but not all of a specific thing
  • Role in causing something to happen
  • verb
  • To make a line in a person's hair, by using a comb
  • To move two things apart creating a space
  • To leave someone, or to break off a relationship

with

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US / wɪð /

UK / wɪð, wɪθ /

A1
  • preposition
  • As an employee of a certain company
  • Against something or someone
  • By using something as a means
  • Due to; because of
  • Including
  • Possessing as a feature
  • Related to
  • (Of the manner/attitude by which you do something)
  • Used to express that people or things are together

from

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US / frəm /

UK / frʌm, frɑm,frəm /

A1
  • preposition
  • Starting at a particular place, time or level

out

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US / aʊt /

UK / aʊt /

A1
  • adverb
  • No longer stylish (e.g. fashion)
  • Away from home, business, or the usual place
  • In a direction/movement away from inside or center
  • noun
  • Act when a batter cannot continue playing
  • verb
  • To tell people a secret

over

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US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

two

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US / tu: /

UK / tu /

A1
  • number
  • 2

manipulate

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US / mə'nɪpjʊleɪt /

UK / məˈnɪpjəˌlet /

B1
  • verb
  • To try to control others to gain an advantage
  • To handle or work in a skillful manner

version

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US / ˈvə:ʃən /

UK / ˈvɚʒən, -ʃən /

A2
  • noun
  • Different way that someone interprets something
  • New or different form of something
  • An updated form of some software

another

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US / əˈnʌðə(r) /

UK / əˈnʌðɚ /

A1
  • adjecitve
  • One more, but not this
  • determiner
  • One more added
  • pronoun
  • One more (thing)

and

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US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

base

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US / beɪs /

UK / bes /

A2
  • noun
  • Place military personnel live, train, and operate
  • Bottom part of an object that touches a surface
  • Unit of counting, e.g. 10 for counting
  • Most important idea or ingredient to add others
  • Origin or start from which something came
  • Main place where an organization or a person works
  • verb
  • To use as the starting point or origin for
  • To have as the main location for (company, etc.)

come

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US / kʌm /

UK / kʌm /

A1
  • verb
  • To arrive at a place
  • (Of mail) to be delivered
  • To move toward someone; go with someone
  • To reach a certain point or state

think

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US / θɪŋk /

UK / θɪŋk /

A1
  • verb
  • To have an idea about something without certainty
  • To have an idea, opinion or belief about something

call

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US / kɔ:l /

UK / kɔl /

A1
  • noun
  • A order or request for action
  • The sound an animal makes, often when in danger
  • A correct prediction, e.g. a decision in a game
  • A short visit to a place or person
  • A decision by a referee or umpire in a game
  • verb
  • To make a request or order for action
  • (Animal) to make sounds to warn of danger
  • To announce the date of an election
  • To make a judgment about something
  • To give someone or something a name
  • To guess in advance the result or outcome
  • To visit a place or person for a short time
  • To phone someone
  • To speak, announce or shout in a loud voice

leave

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US / li:v /

UK / liv /

A1
  • noun
  • Permission to do something
  • Vacation time; time off work
  • verb
  • To go away from; depart
  • To gift property to someone after you die
  • To allow something to continue happening
  • To let something remain unused or available
  • To let something or someone remain somewhere

logarithm

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US / ˈlɒgərɪðəm /

UK / ˈlɔ:gərɪðəm /

A1
  • noun
  • Exponent required to produce a given number

where

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US / hwɛə /

UK / hwɛr, wɛr /

A1
  • conjunction
  • At or in the place which
  • In whatever place
  • pronoun
  • Word you use to ask the location of something

truth

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US / tru:θ /

UK / truθ /

A2
  • noun
  • Real facts about something

once

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US / wʌns /

UK / wʌns /

A1
  • adverb
  • One time; one instance
  • At a time in the past
  • conjunction
  • When; as soon as

complicated

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US / 'kɒmplɪkeɪtɪd /

UK / ˈkɑmplɪˌketɪd /

B1
  • adjecitve
  • Difficult to do, understand or use
  • verb
  • To make more difficult to do, understand or use

straight

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US / streɪt /

UK / stret /

A2
  • adjecitve
  • Not having curves, bends, or angles
  • Not gay; heterosexual
  • honest and direct
  • adverb
  • in a line; immediately; honestly and directly

actually

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US / ˈæktʃuəli /

UK / ˈæktʃuəli /

A1
  • adverb
  • Used to add new (often different) information

realize

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US / 'ri:əlaɪz /

UK / ˈriəˌlaɪz /

A1
  • verb
  • To become aware of or understand mentally

write

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US / raɪt /

UK / raɪt /

A1
  • verb
  • To compose letters and words on paper or a screen
  • To invent or create a computer program
  • To create a song or piece of music

use

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US / ju:s /

UK / ju:s /

A1
  • noun
  • Ability to employ something
  • Need to enable it to work
  • Permission to do something with something
  • Act of spending money
  • Operation of a machine for its function
  • verb
  • To have; to eat, drink, consume etc.
  • To need to operate or work
  • To operate a machine, e.g. a computer
  • To treat a person badly
  • To do something with, for a task or purpose

here

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US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

intuition

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US / ˌɪntjuˈɪʃn /

UK / ˌɪntuˈɪʃən, -tju- /

B2
  • noun
  • Natural ability to guess or feel things

try

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US / traɪ /

UK / traɪ /

A1
  • noun
  • Act of putting the ball over the rugby goal line
  • verb
  • To make an effort, to attempt to do something
  • To examine someone or something in a court of law
  • To test to see if it is good or you like it
  • To make a person go through hardship; test
  • To examine something to see if it works

third

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US / θɜ:d /

UK / θɜ:rd /

A1
  • adjecitve
  • 3rd: Number after second

plus

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US / plʌs /

UK / plʌs /

A2
  • noun
  • A benefit or advantage
  • preposition
  • In addition; add
  • In addition to; Indicates a number above
  • Having a value greater than zero

too

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US / tu: /

UK / tu /

A1
  • adverb
  • In addition, also; with emphasis
  • Say that something is more than you want

already

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US / ɔ:lˈredi /

UK / ɔlˈrɛdi /

A1
  • adverb
  • Having happened or been done before this time

guess

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US / ɡes /

UK / ɡɛs /

A1
  • noun
  • Answer given when you don't know if it is correct
  • verb
  • To give an answer without knowing if it is correct

will

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US / wɪl /

UK / wɪl /

A1
  • noun
  • Desire or choice of someone
  • Document saying who gets your money when you die
  • Strong desire to do something; determination
  • Desire to do something; strong wish to do
  • other
  • Used with verbs to express the future
  • verb
  • To leave property to someone after your death
  • To use mental effort to make something happen
  • Am (is, are) likely to do
  • To influence someone to do something
  • To make something happen by strongly wanting it

become

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US / bɪ'kʌm /

UK / bɪˈkʌm /

A1
  • verb
  • To begin to be; grow to be; develop into
  • To be suitable for a particular job or role

neutral

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US / ˈnju:trəl /

UK / ˈnu:trəl /

B1
  • adjecitve
  • Something with pH value of 7
  • Having no positive or negative electrical charge
  • Not supporting either side in a war, etc.
  • Not taking either side in a debate; not involved
  • noun
  • Color that is dull and not bright, such as gray
  • The rest position for gears in a car or vehicle
  • Person/country not supporting a side in a war, etc.

same

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US / seɪm /

UK / sem /

A1
  • adjecitve
  • Being equal in quality and amount
  • Identical; not different
  • Not changing; constant

apply

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US / ə'plaɪ /

UK / əˈplaɪ /

A1
  • verb
  • To spread a substance or liquid over a surface
  • To commit your time and effort to doing something
  • To make something useful in a certain situation
  • To be relevant for a situation
  • To ask formally for (job, permission etc.)

but

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US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

give

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US / ɡɪv /

UK / ɡɪv /

A1
  • noun
  • Degree of flexibility in something, a material
  • verb
  • To hand over or present something to someone
  • To cause someone to have or experience something

good

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US / ɡʊd /

UK / ɡʊd /

A1
  • adjecitve
  • Proper, appropriate or right
  • (Of an amount) enough; plenty
  • Excellent; high quality
  • Acting well or properly; of moral character
  • In a positive or happy emotional state
  • noun
  • Advantage or benefit

can

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US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

really

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US / ˈri:əli /

UK / ˈriəˌli, ˈrili /

A1
  • adverb
  • Used to stress something that is said; definitely
  • In a true or accurate manner
  • Very

would

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US / wʊd /

UK / wʊd /

A1
  • other
  • Used to indicate something imagined
  • Used to ask or request something politely
  • Verb used to indicate possibility, request etc.
  • Used to indicate a preference
  • Used to indicate a reaction
  • Indicates something that occurred repeatedly
  • Used to indicate willingness or ability to do

alternate

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US / ɔ:lˈtɜ:nət /

UK / ˈɔ:ltərnət /

B2
  • verb
  • To follow one thing after another repeatedly

maybe

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US / ˈmeɪbi /

UK / ˈmebi /

A1
  • adverb
  • Possibly but not certainly; perhaps

our

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US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

not

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US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

quite

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US / kwaɪt /

UK / kwaɪt /

A1
  • adverb
  • Not very; fairly
  • Very; In a complete or total manner

now

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US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

equal

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US / 'i:kwəl /

UK / ˈikwəl /

A1
  • adjecitve
  • Same in shape, size, or number
  • verb
  • To add up or be the same as

want

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US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

original

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US / ə'rɪdʒənl /

UK / əˈrɪdʒənəl /

A2
  • adjecitve
  • Being first made, thought or performed; fresh
  • Being unique or thinking differently from others

they

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US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

add

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US / æd /

UK / æd /

A1
  • verb
  • To include as well
  • To put two things or numbers together, e.g. 2+2

take

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US / teɪk /

UK / tek /

A1
  • noun
  • Filming of a single scene for TV or the movies
  • verb
  • To accept something that is offered
  • To use a method of traveling, e.g. a bus or train
  • To use a camera to make (a photo)
  • To pick up something and go away with it
  • To study a subject in school
  • To attempt to pass (an exam)
  • To require a certain amount of time, money, space

simple

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US / 'sɪmpl /

UK / ˈsɪmpəl /

A1
  • adjecitve
  • Not hard to understand or do; not complex
  • Having only a few parts; not complex
  • Being ordinary or normal
  • Being plain; without a lot added for style

bit

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US / bɪt /

UK / bɪt /

A1
  • noun
  • Device put in a horse's mouth to control it
  • Small piece of something
  • verb
  • (E.g. of fish) to take bait and be caught

rewrite

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US / ˌri:'raɪt /

UK / riˈraɪt /

A2
  • verb
  • To write again to improve, or correct errors

worry

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US / ˈwʌri /

UK / ˈwɜ:ri /

A1
  • noun
  • Something that causes trouble or concern
  • verb
  • To cause concern or trouble over something

way

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US / weɪ /

UK / we /

A1
  • adverb
  • Used to emphasize the amount of something
  • noun
  • Particular aspect of something being thought about
  • One of various choices that could be made
  • Particular existing condition or state
  • (Often long) distance or length of time
  • How something is done
  • Route to go to a place
  • Small street
  • Usual behavior, emotions or habits of someone

confusing

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US / kənˈfju:zɪŋ /

UK / kənˈfjuzɪŋ /

A2
  • adjecitve
  • Being hard to understand
  • verb
  • To make something unclear or hard to understand

log

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US / lɒg /

UK / lɔ:g /

B1
  • noun
  • Detailed account of events and progress on journey
  • Piece of a tree that has fallen or been cut
  • verb
  • To move a certain distance or speed, as recorded
  • To leave a website or computer account
  • To record something in an official account
  • To cut trees down and take the wood to use it

about

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US / ə'baʊt /

UK / əˈbaʊt /

A1
  • adverb
  • To be ready to; going to
  • Nearly; approximately; roughly
  • Near; next to; close to
  • In every direction; in the area of
  • preposition
  • Concerning or of (a topic)

again

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US / ə'ɡen /

UK / əˈɡɛn /

A1
  • adverb
  • One more time, once more

different

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US / ˈdɪfrənt /

UK / ˈdɪfrənt /

A1
  • adjecitve
  • Not of the same kind; unlike other things

even

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US / 'i:vn /

UK / ˈivən /

A1
  • adjecitve
  • Being equal in influence, power, possibility etc.
  • Being divided equally or fairly
  • (Of teams/contest) with similar chances of success
  • Smooth, level, or regular
  • Can be divided by 2; ending in 2, 4, 6, 8, or 0
  • At a regular, equally steady manner
  • Remaining steady and unchanging
  • adverb
  • (When this is surprising) as well; too
  • (Used to compare two things/stress the difference)
  • verb
  • To make something level; to flatten
  • To make something equal

like

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US / laɪk /

UK / laɪk /

A1
  • adjecitve
  • Being equal in status or kind to something else
  • Similar; the same
  • adverb
  • For example
  • preposition
  • Used as a filler; used to ad emphasis
  • In a way similar to the way something is done
  • Such as; for example
  • verb
  • To want to
  • To find something pleasing; to prefer something

people

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US / 'pi:pl /

UK / ˈpipəl /

A1
  • noun
  • Persons sharing culture, country, background, etc.
  • Men, Women, Children

that

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US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

what

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US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

example

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US / ɪgˈzɑ:mpl /

UK / ɪɡˈzæmpəl /

A1
  • noun
  • Thing, person which represents a category

jump

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US / dʒʌmp /

UK / dʒʌmp /

A1
  • noun
  • Large sudden increase
  • An act of springing into the air
  • Bar or other thing that is jumped over
  • A sudden movement due to surprise
  • verb
  • To attack someone suddenly
  • To push your body into the air with your legs
  • To suddenly decide to do something
  • To make a sudden movement due to surprise

least

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US / li:st /

UK / list /

A1
  • adverb
  • In the smallest or lowest way
  • noun
  • Something that is of the lowest or smallest degree

right

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US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

expand

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US / ɪk'spænd /

UK / ɪkˈspænd /

A2
  • verb
  • To make something larger in size, number, amount

mean

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US / mi:n /

UK / min /

A1
  • adjecitve
  • Being good at
  • Nasty; unkind
  • Not liking to spend money; cheap; stingy
  • noun
  • Average of a set of numbers
  • verb
  • To express a particular idea or thought
  • To intend to do something in particular
  • To have a particular meaning or value

frankly

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US / ˈfræŋkli /

UK / ˈfræŋkli /

B2
  • adverb
  • Speaking honestly and directly

must

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US / məst /

UK / mʌst /

A1
  • noun
  • Something that is necessary or required
  • other
  • (Used to state that something ought to be true)
  • Used to say something is required or necessary

then

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US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

first

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US / fɜ:st /

UK / fɚst /

A1
  • adjecitve
  • 1st; Coming before all others in time or place
  • noun
  • Something that has not happened before
  • Position of the winner of a competition

get

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US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

number

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US / ˈnʌmbə(r) /

UK / ˈnʌmbɚ /

A1
  • noun
  • Symbols such as 1, 2, 56, 793
  • Particular song or dance performed during a show
  • Total quantity or amount of things
  • verb
  • To put numbers on things
  • To assign a sequence within a group, series, set
  • To claim to be part of a larger group, series, set

tell

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US / tel /

UK / tɛl /

A1
  • verb
  • To (strongly) advise a person to do something
  • To be able to guess
  • To say or communicate information to someone
  • To inform, but without speaking; indicate
  • To have a negative effect on someone
  • To order someone to do something; command
  • To recognize something based on certain signs
  • To report something to an authority
  • To explain something or teach someone something

for

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US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

time

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US / taɪm /

UK / taɪm /

A1
  • noun
  • Speed at which music is played; tempo
  • Point as shown on a clock, e.g. 3 p.m
  • Number of hours, minutes needed to do something
  • Occasion when something happens
  • Period or occasion that something occurred
  • Period in history or the past
  • Something measured in minutes, hours, days, etc.
  • How long an event takes; duration
  • verb
  • To check speed at which music is performed
  • To choose a specific moment to do something
  • To measure how long an event takes, e.g. a race
  • To schedule something to occur at a specific moment

just

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US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

ask

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US / ɑ:sk /

UK / æsk /

A1
  • verb
  • To say to someone that you want something

start

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US / stɑ:t /

UK / stɑrt /

A1
  • noun
  • First time or place that a thing exists; beginning
  • First opportunity to achieve something, e.g. a job
  • Sudden action or movement because you are scared
  • other
  • Beginning of something in place or time
  • verb
  • To do, be or happen for the first time; begin
  • To turn something on

well

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US / wel /

UK / wɛl /

A1
  • adjecitve
  • Being in a fortunate, good condition or state
  • Healthy and in good condition
  • adverb
  • In an acceptable, proper, or successful manner
  • In a complete, total, or full manner
  • A great and considerable degree
  • In a successful way, in a good or satisfactory way
  • exclamation
  • Used to begin or continue a particular statement
  • Used to show you want to start saying something
  • Used to express that you are waiting for a reply
  • You say this to change the topic of a conversation
  • Used to indicate you are making a final remark
  • noun
  • Long deep hole in the ground to get water
  • verb
  • To cause your eyes to fill with tears

statement

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US / ˈsteɪtmənt /

UK / ˈstetmənt /

A2
  • noun
  • Record of activity in a bank account over time
  • Act or process of saying something formally

much

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US / mʌtʃ /

UK / mʌtʃ /

A1
  • adjecitve
  • Very; to a high level or degree
  • adverb
  • A lot; large amount; a high degree of
  • Nearly; basically
  • On many occasions; often
  • noun
  • A large amount; a great quantity

green

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US / gri:n /

UK / ɡrin /

A1
  • adjecitve
  • Color of young leaves
  • Covered with vegetation, e.g. grass
  • Concerned about protecting the environment
  • The color of young leaves
  • Lacking in experience/knowledge due to being young
  • Being not fully grown or ripe, as in fruit
  • noun
  • Large grassy area
  • used as a part of a name of a place (UK)

shoot

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US / ʃu:t /

UK / ʃut /

A2
  • noun
  • Emerging new part of a plant
  • verb
  • To kick or throw a ball at a goal
  • To fire a gun; injure or kill someone with a gun
  • To (cause to) fly away forcefully
  • To use a camera to record a film/take a photograph

equation

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US / ɪˈkweɪʒn /

UK / ɪˈkweʒən, -ʃən /

B1
  • noun
  • Mathematical statement showing things to be equal
  • Complex set of different facts, ideas or issues
  • Subtitles section
  • We're asked to simplify log base 3 of 27x.
  • And frankly, this is already quite simple.
  • But I'm assuming they want us to use some logarithm properties and manipulate this in some way, maybe to actually make it a little bit more complicated.
  • But let's give our best shot at it.
  • So the logarithm property that jumps out at me-- because this right over here-- we're saying what power do we have to raise 3 to to get 27x?
  • 27x is the same thing as 27 times x.
  • And so the logarithm property it seems like they want us to use is log base-- let me write it-- log base b of a times c-- I'll write it this way-- log base b of a times c.
  • This is equal to the logarithm base b of a plus the logarithm base b of c.
  • And this comes straight out of the exponent properties that if you have two exponents, two with the same base, you can add the exponents.
  • So let me make that a little bit clearer to you.
  • And if this part is a little confusing, the important part for this example is that you know how to apply this.
  • But it's even better if you know the intuition.
  • So let's say that log base b of a times c is equal to x.
  • So this thing right over here evaluates to x.
  • Let's say that this thing right over here evaluates to y.
  • So log base b of a is equal to y.
  • And let's say that this thing over here evaluates to z.
  • So log base b of c is equal to z.
  • Now, what we know is, this thing right over here or this thing right over here tells us that b to the x power is equal to a times c.
  • Now, this right over here is telling us that b to the y power is equal to a.
  • And this over here is telling us that b to the z power is equal to c.
  • Let me do that in that same green.
  • So I'm just writing the same truth.
  • I'm writing it as an exponential function or exponential equation, instead of a logarithmic equation.
  • So b to the zth power is equal to c.
  • This is the same statement or the same truth said in a different way.
  • And this is the same truth said in a different way.
  • Well, if we know that a is equal to this, is equal to b to the y, and c is equal to bz, then we can write b to the x power is equal to b to the y power-- that's what a is.
  • We know that already-- times b to the z power.
  • And we know from our exponent properties that if we take b to the y times b to the z, this is the same thing as b to the-- I'll do it in a neutral color-- b to the y plus z power.
  • This comes straight out of our exponent properties.
  • And so if b to the y plus z power is the same thing as b to the x power, that tells us that x must be equal to y plus z.
  • If this is confusing to you, don't worry about it too much.
  • The important thing, or at least the first important thing, is that you know how to apply it.
  • And then you can think about this a little bit more, and you can even try it out with some numbers.
  • You just have to realize that logarithms are really just exponents.
  • I know when people first would tell me that, I was like, well, what does that mean?
  • But when you evaluate a logarithm, you're getting an exponent that you would have to raise b to to get to a times c.
  • But let's just apply this property right over here.
  • So if we apply it to this one, we know that log base 3 of 27 times x-- I'll write it that way-- is equal to log base 3 of 27 plus log base 3 of x.
  • And then this right over here, we can evaluate.
  • This tells us, what power do I have to raise 3 to to get to 27?
  • You could view it as this way.
  • 3 to the ?
  • is equal to 27.
  • Well, 3 to the third power is equal to 27.
  • 3 times 3 is 9 times 3 is 27.
  • So this right over here evaluates to 3.
  • So if we were to simplify-- or I guess I wouldn't even call it simplifying it.
  • I would just call it expanding it out or using this property, because we now have two terms where we started off with one term.
  • Actually, if we started with this, I'd say that this is the more simple version of it.
  • But when we rewrite it, this first term becomes 3.
  • And then we're left with plus log base 3 of x.
  • So this is just an alternate way of writing this original statement, log base 3 of 27x.
  • So once again, not clear that this is simpler than this right over here.
  • It's just another way of writing it using logarithm properties.