Chapter 3 Review

Transformers

100

What does a logarithm help us find?

An exponent

200

Write the log equation in its equivalent exponential form:

3=log₄x

4³=x

300

Write the log equation in its equivalent exponential form:

(1/2)=log₄₉7

49^(1/2)=7

400

Write the exponential equation in its logarithmic form:

6³=216

log₆216=3

500

Write the exponential equation in its equivalent logarithmic form:

x^3x+2=17

log_x17=3x+2

All about that Base

100

Which type of logarithm has a base of 10?

Common logarithms

200

Which type of logarithm has a base of e?

Natural logarithms

300

Write the following expression so that both sides have the same base:

2³=16^x

2³=2^4x

400

Write the following expression so that both sides have the same base:

27^x+3=9

3^3x+9=3²

500

Write the following expression so that both sides have the same base:

25^x-2=125^2x+3

5^2x-4=5^6x+9

Don't break the rules

100

Evaluate the expression:

log₄64

3

200

Evaluate the expression:

log₃3⁸

8

300

Evaluate the expression:

log₃(1/27)

-3

400

Evaluate the following expression:

ln e⁵

5

500

Evaluate the following expression:

log₃(log₈8)

0

We're all in this together

100

What are the names of the three rules we use to expand and condense logs?

Product, Quotient, Power

200

Expand the following log as much as possible:

log₆(36x³)

2 + 3 log₆x

300

Expand the following log as much as possible:

log₂((xy²)/64)

log₂x + 2 log₂y - 6

400

Condense the following log as much as possible:

log_b7+log_b3

log_b21

500

Condense the following log as much as possible:

(1/2) log₅x - log y

Cannot condense

I can't find my x

100

Solve the given equation:

2^4x-2=64

x=2

200

Solve the given equation:

9^x+2=27^-x

x=-4/5

300

Solve the given equation:

e^12-5x-7=123

x=1.43

400

Solve the given equation:

3 + 4 ln(2x)=15

x=10.04

500

Solve the given equation:

log₃(x-1) - log₃(x+2) = 2

x=-19/8