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 $6$ must be raised to get $1.$ $$\begin{array}{c}{\log }_6(1)=y\iff 1=6^y\end{array}$$ Therefore, we should rewrite $1$ as a power of $6$ and the resulting exponent will be our answer. Thus, ${\log }_6(1)=0.$