Chapter 12 - Exponential Functions and Logarithmic Functions - 12.3 Logarithmic Functions - 12.3 Exercise Set - Page 803: 82

$x=2$

Converting to exponential form, the given logarithmic equation, $ \log_5{25}=x ,$ is equivalent to \begin{array}{l}\require{cancel} 5^x=25 \\\\ 5^x=5^2=25 .\end{array} We have now found what value x makes the above statement, $5^x=25$, true: \begin{array}{l}\require{cancel} x=2 .\end{array}