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Chapter 11 part 1:

How can a logarithmic functions be rewritten as its inverse (exponential function)?

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Answer:

  [tex]\text{for }f(x)=\log_b(x),\text{ the inverse is }f^{-1}(x)=b^x[/tex]

Step-by-step explanation:

As with any function and its inverse, you can find the inverse of ...

  [tex]f(x)=\log_b(x)[/tex]

by solving the equation x = f(y).

  [tex]x=\log_b(y)\\\\b^x=y\qquad\text{use as a power of b}\\\\\boxed{f^{-1}(x)=b^x}[/tex]

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