Log 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 log₈ 1/512 = -3?

400

Write in log form: 16^-2 = 1/256

What is log₁₆ 1/256 = -2?

500

Write in log form: 7³ = 343

What is log₇ 343 = 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: log₁₅ 1/3,375= -3

What is 15^-3= 1/3,375?

400

Write in exponential form: log₉ 3=1/2

What is 9 ^1/2 = 3?

500

Write in exponential form: log_10,000 1/1,000 = -3/4

10,000^-3/4 = 1/1,000

Log Expressions

100

log₂₀400

What is x=2?

200

log₅ 15,625

What is x=6 ?

300

log₆ 1/7,776

What is x= -5?

400

log₈ 16,777,216

What is x= 8 ?

500

log₁₆ 1

What is x = 0?

Expand and Condense

100

Condense

log (x) + log (y)

log (xy)

200

Condense

log (16) + log (2) + log (3)

log 96

300

Expand

log (yx³)

log(y) +3log(x)

400

Condense

log(x+2) + log(x-3)

log(x²-x-6)

500

log_4x-log_4(3)+2log_4y

log_4((xy^2)/3)

Solve

100

Solve:

log(36)-log(y)=log (12)

y=3

200

7^x=250

x=2.84

300

(1/6)^(2x)= 36^(x-2)

x=1

400

log_3x+log_3(x-6)=3

x=9

(x=-3 is extraneous)

500

log_(1/4)x=-3

x=64