Chapter 12 - Exponential Functions and Logarithmic Functions - Review Exercises: Chapter 12 - Page 843: 24

The equivalent logarithmic equation for the exponential equation is: ${{2}^{-3}}=\frac{1}{8}$ is $-3={{\log }_{2}}\frac{1}{8}$.

${{2}^{-3}}=\frac{1}{8}$ The function ${{2}^{-3}}=\frac{1}{8}$ is in the form ${{a}^{m}}=x$. Here, $m=-3,a=2\text{ and }x=\frac{1}{8}$ Thus, the equivalent logarithmic equation is ${{\log }_{a}}x=m$. This gives: $-3={{\log }_{2}}\frac{1}{8}$.