Question

How do you evaluate ${\log }_{0.01}\left(10\right)$

Answer 1

Calculate the value of ${\log }_{0.01}10$

Let ${\log }_{0.01}10=x$

$$\begin{gathered} {(0.01)}^x=10 \\ {\left({10}^{-2}\right)}^x={10}^1 \\ {10}^{-2x}={10}^1 \end{gathered}$$

Compare L.H.S and R.H.S

$$\begin{gathered} \Rightarrow -2x=1 \\ x=-\frac{1}{2} \end{gathered}$$

Hence the answer is $x=-\frac{1}{2}$