Converting Logarithms and Exponential Functions

Change to Logarithmic Form:
12² = 144

• log ₂ 144 = 12

• log ₁₂ 144 = 2

• log ₁₂ 2 = 144

• log ₂ 12 = 144

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Rewrite log_vn = a in exponential form.

• v^a = n

• n^a = v

• vⁿ = a

• aⁿ = v

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Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81

• log₈₁3 = 4

• log₃81 = 4

• log₄81 = 3

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How are exponentials and logarithms related?

• They're cousins

• They're inverses

• They're not related

• They're reciprocals

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Converting exponential to logarithmic form: Write the logarithmic form of the exponential equation 3^x = 27

• log3(3) = x

• log3(9) = x

• log27(3) = x

• log3(27) = x

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Converting exponential to logarithmic form: Convert the exponential equation 5^2 = 25 to logarithmic form

• log2(25) = 5

• log5(2) = 25

• log25(5) = 2

• log5(25) = 2

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Write b^k = m into logarithmic form.

• log _b m = k

• log _m k = b

• log _b k = m

• log _k m = b

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Solving exponential equations using logarithms: Solve the equation 2^x = 16 using logarithms

• x = 4

• x = 8

• x = 10

• x = 2

Solving exponential equations using logarithms: Find the value of x in the equation 4^x = 64 using logarithms

• 16

• 3

• 8

• 2

log₆(2x + 3) = 3

• x = 106.5

• x = 100

• x = 16

• x = 50

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