Question

Convert the equation from exponential to logarithmic form:

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

Short answer

On converting the equation we get,

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

Step-by-step solution

Step 1. Given information.

Consider the given equation,

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

Compare the given equation with the standard form $x=a^y$, we get,

$$\begin{gathered} a=10, \\ y=-2, \\ x=\frac{1}{100} \end{gathered}$$

Step 2. Convert into logarithmic form.

Convert exponential form in logarithmic form,

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

Therefore, we get,

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