# How do you evaluate log_(1/6) (1/6)?

Consider what power the base $\left(\frac{1}{6}\right)$ must be raised to, to obtain $\frac{1}{6}$
That is ${\left(\frac{1}{6}\right)}^{1} = \frac{1}{6}$ hence value is 1.
In general $\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{\log}_{b} \left(b\right) = 1} \textcolor{w h i t e}{\frac{a}{a}} |}}}$