Logarithms

Express in Exponential form

100

log₅ 125 = 3

5³ = 125

200

log₅ 1 = 0

5⁰ = 1

300

log 0.01 = -2

10^-2 = 0.01

400

log_1/4 4 = -1

(1/4)^-1 = 4

500

log₂₇ 9 = 2/3

27^2/3 = 9

Express in logarithmic form

100

4³ = 64

log₄ 64 = 3

200

6³ = 216

log₆ 216 = 3

300

8^-2/3 = 1/4

log₈ 1/4 = -2/3

400

6^-2 = 1/36

log₆ 1/36 = -2

500

e^x = 4

ln 4 = x

Evaluate or Solve

100

log₃ 1/27

-3

200

log₄ 16 = 2x - 2

x = 2

300

log₃ √27

3/2

400

log₄ 1/4 = x/8

x = -8

500

36^2x = 216^x-1

x = -3

Sum or Difference of Logs

100

log₆ x³

3 log₆ x

200

log₃ √5

1/2 log₃ 5

300

log_b 2x²y³

log_b 2 + 2 log_b x + 3 log_b y

400

log_b (x/4)^2y

2y log_b x - 4y log_b 2

500

log_b (7x³y²/√z)

(log_b 7 + 3 log_b x + 2 log y) - 1/2 log z

Single Logarithm

100

log₂ 4 - log₂ 16

log₂ 4/16 or -2

200

5 log₃ 3 - log₃ 9

log₃ 243/9 or 3

300

(log₂ x + log₂ y) - log₂ z

log₂ xy/z

400

log₅ x - 1/5 log₅ y

log₅ x/⁵√y

500

log₃ y + 4 log₃ t⁴

log₃ yt¹⁶