Chapter 12 - Exponential Functions and Logarithmic Functions - Review Exercises: Chapter 12 - Page 843: 25

The equivalent logarithmic equation for the exponential equation ${{25}^{\frac{1}{2}}}=5$ is $\frac{1}{2}={{\log }_{25}}5$.

${{25}^{\frac{1}{2}}}=5$ The function ${{25}^{\frac{1}{2}}}=5$ is in the form ${{a}^{m}}=x$, Here, $m=\frac{1}{2},a=25\text{ and }x=5$. Thus, the expression can be written in the form $m={{\log }_{a}}x$, that is $\frac{1}{2}={{\log }_{25}}5$.