# Chapter 9 - Section 9.5 - Logarithmic Functions - Exercise Set: 93c

$f(25)=2$

#### Work Step by Step

We are given that $f(x)=log_{5}x$ and that $g(x)=5^{x}$ is the inverse of $f(x)$. We are also told that the ordered pair (2,25) is a solution of the function $g(x)$. As seen in Section 9.2, when the ordered pair $(x_{1},y_{1})$, is a solution to a function, that function's inverse will have a solution of $(y_{1},x_{1})$. Therefore, the ordered pair $(25,2)$ will be a solution of $f(x)$. We write this in function notation as $f(25)=2$, which tells us that $f(x)$ has a value of 2 when $x=25$. $f(25)=log_{5}25=2$

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