Question

Convert from exponential to logarithmic form:

${\left(\frac{1}{3}\right)}^4=\frac{1}{81}$.

Short answer

The logarithmic form is,

$4={\log }_{\frac{1}{3}}\left(\frac{1}{81}\right)$.

Step-by-step solution

Step 1. Given the information.

The exponential form is,

${\left(\frac{1}{3}\right)}^4=\frac{1}{81}$.

Step 2. Converting to logarithmic form.

$$\begin{gathered} {\left(\frac{1}{3}\right)}^4=\frac{1}{81} \\ y={\log }_a\left(x\right) \\ 4={\log }_{\frac{1}{3}}\left(\frac{1}{81}\right). \end{gathered}$$

If ${\left(\frac{1}{3}\right)}^4=\frac{1}{81}$,

then$4={\log }_{\frac{1}{3}}\left(\frac{1}{81}\right)$.