Evaluating Logarithms

To evaluate the given logarithm, we can rewrite it as an exponential equation by using the definition of a logarithm. $$\begin{array}{c}{\log }_{b}x=y\iff x=b^y\end{array}$$ The above means that the logarithm $y$ is the exponent to which $b$ must be raised to get $x.$ For our exercise, $y$ is the exponent to which $7$ must be raised to get $49.$ $$\begin{array}{c}{\log }_{7}49=y\iff 49=7^y\end{array}$$ Therefore, we should rewrite $49$ as a power of $7$ and the resulting exponent will be our answer. $$\begin{array}{c}49\iff 7^2\end{array}$$ Thus, ${\log }_7(49)=2.$