Converting between Log and Exponential Form

• 9^x=2

• 2^x=9

• 2⁹=x

• 9²=x

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CCSS.HSF.BF.B.5

Write 6^x = 8 in log form

• log₆ 8 = x

• log₈ 6 = x

• log₆ x = 8

• log₈ x = 6

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CCSS.HSF.BF.B.5

• 5^x = 3

• log₃ 5 = log₃ x

• x⁵ =3

• 3⁵ = x

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CCSS.HSF.BF.B.5

Convert 3^x = 12 to the equivalent log form

• 3¹² = x

• log_x 3 = 12

• log₃ x = 12

• log₃ 12 = x

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CCSS.HSF.BF.B.5

Write 5^x =10 in log form

• x = log 5

• x = log₅10

• x = 5 log10

• x = 10 log 5

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CCSS.HSF.BF.B.5

Change to exponential form.

log_x 2 = 5

• x² = 5

• 5² = x

• x⁵ = 2

• 2⁵ = x

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CCSS.HSF.BF.B.5

Write 3 = 7^x in log form.

• log₇ 3 = x

• log₃ 7 = x

• log₇ x = 3

• log₃ x = 7

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CCSS.HSF.BF.B.5

Rewrite 3⁴ = 81 in logarithmic form.

• log₃ 4 = 81

• log₈₁ 3 = 4

• log₃ 81 = 4

• log₄ 81 = 3

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CCSS.HSF.BF.B.5

Change to Exponential Form:
log₆ 36 = 2

• 2⁶ = 36

• 6² = 36

• 36² = 6

• 36⁶ = 2

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CCSS.HSF.BF.B.5

14² = 196

Convert to log form

• log₁₄ 196 = 2

• log₂ 14 = 196

• log₂ 196 = 14

• log₁₄ 14 = 2

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CCSS.HSF.BF.B.5