Exponential and Logarithmic Functions as Inverses

The exponential function f(x)=2^x and the logarithmic function g(x)=log₂(x) are inverses. You know that because their graphs are reflected over what line?

• the x-axis

• the y-axis

• y=x

• y=-x

A logarithmic function is the inverse of an exponential function.

• True

• False

Which equation is the inverse of the equation above?

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Which equation is the inverse of the equation above?

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What is the inverse of f(x)=5^x+3?

• f^-1(x)=log₃(x-5)

• f^-1(x)=log₅(x)-3

• f^-1(x)=log₅(x-3)

• f^-1(x)=log₅(x+3)

Which equation is the inverse of the equation above?

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Which equation is the inverse of the equation above?

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Which equation is the inverse of the equation above?

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How are exponential and logarithmic functions related?

• Opposites

• Inverses

• Cousins

• Reciprocals

Change to Logarithmic Form:

5³ = 125

• log ₅ 125 = 3

• log ₃ 125 = 5

• log ₅ 3 =125

• log₁₂₅ 3 = 5