Which function is the inverse of f(x)=log13 x

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1 answer

To find the inverse of the function \( f(x) = \log_{13}(x) \), we start by replacing \( f(x) \) with \( y \):

\[ y = \log_{13}(x) \]

Next, to find the inverse, we swap \( x \) and \( y \):

\[ x = \log_{13}(y) \]

Now, we need to solve for \( y \). We can rewrite the logarithmic equation in its exponential form:

\[ y = 13^x \]

Thus, the inverse function is:

\[ f^{-1}(x) = 13^x \]

So, the inverse of \( f(x) = \log_{13}(x) \) is \( f^{-1}(x) = 13^x \).