Question

Convert from exponential to logarithmic form:

${10}^{-2}=\frac{1}{100}$.

Short answer

The logarithmic form is,

$2={\log }_{\frac{1}{10}}\left(\frac{1}{100}\right)$

Step-by-step solution

Step 1. Given the information.

The exponential form is,

${10}^{-2}=\frac{1}{100}$.

Step 2.Converting to logarithmic form.

$$\begin{gathered} {10}^{-2}=\frac{1}{100} \\ {\left(\frac{1}{10}\right)}^2=\frac{1}{100} \\ y={\log }_a\left(x\right) \\ 2={\log }_{\frac{1}{10}}\left(\frac{1}{100}\right) \end{gathered}$$

If ${10}^{-2}=\frac{1}{100}$

then$2={\log }_{\frac{1}{10}}\left(\frac{1}{100}\right)$.