Logarithms

Rewrite log₂8 = 3 in exponential form

• 2⁸ = 3

• 2³ = 8

• 3² = 8

• 8³ = 2

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81
• log₈₁3 = 4
• log₃81 = 4
• log₄81 = 3

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

Write in exponential form

log₂32 = 5

• 2^-5 = 32

• 2³² = 5

• 2⁵ = 32

• 32⁵ = 2

Solve for x.
3^x = 27

• 2
• 4
• 3
• 5

Evaluate.
log₃81

• 4
• ¹/₄
• -4
• -¹/₄

Write the logarithm expression as a single logarithm

log₄60 - log₄4 + log₄x

• log₄15

• log₄15x

• log₄56x

• xlog₄30

Write the logarithm expression as a single logarithm

2log 4 + log 2

• log 8

• log 16

• log 32

• log 8²

Write as one logarithm. Simplify, if possible.

log₃9 + log₃27

• log₃3

• log₃243

• log₃1/3

• not possible

Expand the logarithm expression

log₅5x^-5

• -5(log₅5x)

• -5log₅5 + log₅x

• log₅25x

• log₅5 - 5log₅x