5.1.2 Inverse functions in Logarithmic form

Rewrite log₂8 = 3 in exponential form.

• 2⁸ = 3

• 2³ = 8

• 3² = 8

• 8³ = 2

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Write 8 = 2³ in logarithmic form.

• 3 = log₂ 8

• 8 = log₂ 3

• 2 = log₃ 8

• 8 = log₃ 2

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Write 4 = log₃ 81 in exponential form.

• 3 = 81⁴

• 4 = 81³

• 81 = 4³

• 81 = 3⁴

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Write 10⁴= 10000 in logarithmic form.

• log₁₀ 4 = 10000
• log₁₀₀₀₀ 4 = 10
• log₁₀ 10000 = 4
• log₄ 10000 = 10

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Logarithmic functions are the inverse of...

• Linear Functions
• Exponential Functions 
• Quadratic Functions 
• Polynomial Functions 

Evaluate: log₆₄4 = x

• x = 3

• x = -3

• x = ⅓

• x = -⅓

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Convert 6^(x+2)=216 to logarithmic form

• log₂₁₆(x+2)=6
• log₆(x+2)=216
• log₆(216)=x+2
• log_(x+2)(216)=6

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Write in exponential form.

5 = log₂32

• 32 = 2^-5 = 32

• 5 = 2³²

• 32 = 2⁵

• 2 = 32⁵

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Convert 10^(x+5)=100 to logarithmic form.

• log₁₀₀=x+5
• log₁₀(x+5)=100

• log₁₀(100)=x+5

• log_(x+5)(100)=10

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Solve for x:
log₄ x = 3

• 4
• 12
• 32
• 64

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