Logarithms Review

Exponential Equations

100

2³ = 2^x

x = 3

200

7^3x+2 = 7^x-1

x = -3/2

300

1 = 6^2x-6

x = 3

400

5^x-1 = 125

x = 4

500

Solve for x.

2^2x+5 = 1/8

x = -4

Exponential and Logarithmic Form

100

Convert to exponential form. 

log₂8 = 3

2³ = 8

200

Convert to logarithmic form.

3⁵ = 243

log₃243 = 5

300

Convert to exponential form. 

log_m10 = n

mⁿ = 10

400

Convert to logarithmic form. 

x⁷ = y

log_xy = 7

500

How would you solve the following equation for x in your calculator (what would you type using logs)?

5^x = 1.5

log(1.5)/log(5)

Evaluate Logarithms

100

log₃81

4

200

log₁₈18

1

300

log₅1

0

400

log₆(1/36)

-2

500

log₁₂₅5

1/3

Properties of Logarithms

100

Expand log₈(cd)

log₈(c) + log₈(d)

200

Condense log₂(7)-log₂(9)

log₂(7/9)

300

Condense 8*log₃r

log₃r⁸

400

Fully expand log₇(3*x/y)

log₇(3) + log₇(x) - log₇(y)

500

Fully expand ln(xy²)

ln(x) + 2*ln(y)

Logs in the Calculator

100

Find log(1000)

3

200

Find ln(1.5)

Round your answer to the nearest hundredth.

.41

300

Find log₅7

Round your answer to the nearest hundredth

1.21

400

What is g(2) if g(x) = log₃(x+1) - 5 ?

-4

500

What is the domain of the function f(x) = 3*2^x ?

x>0