Unit 2 Review

Vocab

100

what is the value of the log if the base and the argument are the same?

1

200

if the argument is 1, what is the value of the log

0

300

if the argument is a common fraction, what sign will the answer have?

negative

400

if the arguments are equal, the log with the smaller base will be larger or smaller?

larger

500

what is the notation for estimating a log? use variables x and y 

it is between x and y but closer to x/y

Properties of Log

100

T or F: logarithms are continuous and increasing from 0 to infinity

True

200

which value is the argument: log₂5

5

300

how can you expand this log based off the power rule: logx³

3logx

400

how can you expand this function using the product rule: log(ab)

log a + log b

500

how do you expand this expression using the quotient rule: log(a/b)

log a - log b

graphing logs

100

describe the transformations: -2 + log(x-3)

down two units, to the right 3 units

200

where is the vertical asymptote for logs?

x = 0

300

what is the domain of a log?

(0,infinity)

400

what is the range of a log?

all real numbers or (-infinity, infinity)

500

describe the transformation: log(x+3) +4

up 4 units, to the left 3 units

e

100

T or F: e is an irrational number

true

200

what is the value of e? i need at least 3 decimal places.

2.718281828...

300

T or F: the domain/range for e is all real numbers

False, the domain is all real numbers but the range for e is (0,infinity), e cannot have any negative numbers

400

what is the inverse of e?

natural log (ln)

500

T or F: e is increasing over the entire domain and has the same shape as y=3^x

True, it is similar to 3 since e = 2.7 and is increasing

inverses

100

what is the inverse of x-3

x+3

200

what is the inverse of 3x

x/3

300

what is the inverse of x²

square root of x

400

what is the inverse of y=3x+9

y = (x-9) / 3

500

what is the inverse of 2y = 2x - 10

y = x - 5