Unit 7 Logarithms Review

Convert log<->exponent

100

Convert from exponential form to logarithmic form:

4⁵ = 1024

log₄ 1024 = 5

200

Convert from logarithmic form to exponential form:

log₅ 125 = 3

5³ = 125

300

Convert from logarithmic form to exponential form:

log 10 = 1

10¹ = 10

400

Convert from exponential form to logarithmic form:

(1/2)^-4 = 16

log_1/2 (16) = -4

500

Convert from logarithmic form to exponential form:

log (1/100) = -2

10^-2 = 1/100

Evaluate

100

Evaluate: log₃ 27

3

200

Evaluate: log₅ 25

2

300

Evaluate: log₂₇ 3

1/3

400

Evaluate: log₄ 4096 + log₄ 64

9

500

Evaluate: log₂ 32 + log₃ 243

10

Expand or Simplify

100

Simplify: 9 log₃ x

log₃ x⁹

200

Expand: log₅ 2a²b

log₅ 2 + 2 log₅ a + log₅ b

300

Expand: log (x²y³/z)

2 log x + 3 log y - log z

400

Simplify: 2 log₅ x + 3 log₅ y - 4 log₅ z

log₅ (x²y³/z⁴)

500

Simplify: 5 log₄ x + 4 log₅ x - 3 log₄ x

log₄ x² + log₅ x⁴

Solve

100

Solve: log₃ (3x - 1) =  log₃ (x + 5) 

x = 3

200

Solve: log₂ x + log₂ 3 = 4 (exact value)

x = 16/3

300

Solve: 2^x+1 = 7 (3 significant figures)

x = 1.81

400

Solve: 2 (3^2t-5) - 4 = 10 (3 decimal places)

t = 3.386

500

Solve: log 5x + log (x + 1) = 2

x = 4