Chapter 6.4, Problem 12Q

To determine

To write: The expression ${\log }_{1/3}27=-3$ in an exponential form or logarithmic form.

Answer to Problem 12Q

The expression ${\log }_{1/3}27=-3$ can be written as $3^3=27$ in exponential form.

Explanation of Solution

Given information:

The expression is ${\log }_{1/3}27=-3$ .

Calculation:

Consider the given expression.

  ${\log }_{1/3}27=-3$

Arrange the expression.

  $\begin{array}{c}{\log }_{1/3}27=-3\\ 27={\left(\frac{1}{3}\right)}^{-3}\left\{\begin{array}{r}\text{Property}\\ {\log }_a^{}x=y\\ x=a^y\end{array}\right\}\\ 27=\frac{1}{3^{-3}}\\ 3^3=27\end{array}$

Therefore, the expression ${\log }_{1/3}27=-3$ can be written as $3^3=27$ in exponential form.