Logarithm Review

Exponential to Log

100

Write in log form: 4² = 16

What is log₄16 = 2?

200

Write in log form: 7⁴ =2,401

What is log₇2,401 = 4?

300

Write in log form:  8^-3 = 1/512 

What is

log_8 (1/512) = -3

?

400

Write in log form:

16^ (-3/2) = 1/64

What is

log_16 (1/64) = -3/2 

?

500

Write in log form:  27^(5/3) = 243 

What is

log_27 243 = 5/3

?

Log to Exponential

100

Write in exponential form: log₅ 125=3

What is 5³ = 125?

200

Write in exponential form: log₂₆ 676=2

What is 26² = 676?

300

Write in exponential form:  log_15 (1/3375)= -3 

What is

15^-3= 1/3375

?

400

Write in exponential form: 

log_9 3= 1/2

What is

9 ^(1/2) = 3

?

500

Write in exponential form:  log_10000 (1/1000) = -3/4 

10000^(-3/4 )= 1/1000

Log Expressions

100

Evaluate log₂₀400

What is x=2?

200

Evaluate log₅ 15,625

What is x=6 ?

300

Evaluate  log_6 (1/7776) 

What is x= -5?

400

Evaluate log₈ 16,777,216

What is x= 8 ?

500

Evaluate log₁₆ 1

What is x = 0?

Solve Log Equations

100

Solve the equation: log₄₂₀(x+1)=log₄₂₀(70)

What is 69?

200

loga + log 10 = log520

a = 52

300

ln (x-6)=1

x = e+6 or x = 8.72

400

log_4 (x^2-5x+1)=log_4(x-4)

x=5

500

The half-life of radon-222 is 3.8 days. How much of a 100 gram sample is left after 15.2 days?

6.25 grams

Properties of Logarithms

100

Expand 

log_6 (7a)

log_6 7 +log_6 a

200

Expand  log (7/x) 

log7-log x

300

Expand 

lny^4

4lny

400

Expand  ln 3x^8 

ln3+8lnx

500

Solve the following equation:   log_4 2x^2 +log_4 3= log_4 24 

x = +-2