Evaluate a Logarithm

Rewrite log₂8 = 3 in exponential form

• 2⁸ = 3

• 2³ = 8

• 3² = 8

• 8³ = 2

Rewrite the equation into logarithmic form:
6² = 36

• log₆ 2 = 36
• log₆ 36 = 2
• ln 36 = 2
• 6³⁶ = 2

Write in exponential form.
log₂(¹/₈) = -3

• 2^-3 = ¹/₈
• 2^1/8 = -3
• -3² = ¹/₈
• -3^1/8 = 2

Write in logarithmic form

2^-4 = ¹/₁₆

• log₂(¹/₁₆) = -4

• log_-4(¹/₁₆) = 2

• log _-4 2 = ¹/₁₆

• log₂(-4) = ¹/₁₆

To evaluate a logarithm statement log₉81, you think "9 to what power is 81".

• True, and it's 2

• False

Evaluate the log by thinking " 3 to what power is 1/9" so

log₃(1/9) =

• 1/2

• 2

• -2

• 3

Evaluate by thinking 4 to what power is 16, so

log₄16

• 2

• 4

• 1/2

• -2

True or False: log₈64=2

• True
• False

Evaluate log₈ 8 by thinking 8 to what power is 8, so the answer is

• 8

• -1

• 0

• 1

Evaluate log_b(b)

• -1
• 0
• 1
• b