Converting Between Exponents and Logs

Rewrite log₂8 = 3 in exponential form.

• 2⁸ = 3

• 2³ = 8

• 3² = 8

• 8³ = 2

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Change to Exponential Form:
log₆36 = 2

• 2⁶=36

• 6²=36

• 36²=6

• 36⁶=2

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CCSS.HSF.BF.B.5

log_n117 = 11

• n¹¹ = 117

• 11ⁿ = 117

• 117ⁿ = 11

• n¹¹⁷ = 11

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CCSS.HSF.BF.B.5

n^m = 156

• log_n 156 = m

• log_n m = 156

• log_m 156 = n

• log_n 16 = n

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CCSS.HSF.BF.B.5

Rewrite in exponential form: 
2=log₉x

• 9^x=2

• 2^x=9

• 2⁹=x

• 9²=x

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CCSS.HSF.BF.B.5

Convert to exponential form: \log_8\left(\frac{1}{64}\right)=-2

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CCSS.HSF.BF.B.5

Convert to logarithmic form: 2^9=512

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CCSS.HSF.BF.B.5

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CCSS.HSF.BF.B.5

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Convert to logarithmic form: 6^1=6

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CCSS.HSF.BF.B.5