Convert Between Logs and Exponents

Write in logarithmic form:

a^b = c

• log _a c = b

• log _b c = a

• log _a b = c

• log _b a = c

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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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Change to Logarithmic Form:
5³ = 125

• log ₅ 125 = 3

• log ₃ 125 = 5

• log ₅ 3 =125

• log₁₂₅ 3 = 5

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Rewrite in exponential form:

log₉x=2

• 9^x=2

• 2^x=9

• 2⁹=x

• 9²=x

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Write 5^x =10 in log form

• x = log 5

• x = log₅10

• x = 5 log10

• x = 10 log 5

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Mathematical Equivalence

ON

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Write 6^x = 8 in log form.

• log₆ 8 = x

• log₈ 6 = x

• log₆ x = 8

• log₈ x = 6

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A logarithm is the inverse function of

• a quadratic.

• an exponential.

• a linear function.

• a cubic.

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Logarithms and Exponentials are what?

• parallel

• perpendiular 

• inverses

• congurent

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Rewrite log₃t = 5 in exponential form.

• 5^t=3

• log₃5 = log₃t

• t⁵=3

• 3⁵=t

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