Chapter 6.4, Problem 14Q

To determine

Towrite:Theexpression $4^{-2}=0.0625$ in an exponential form or logarithmic form.

Answer to Problem 14Q

The expression $4^{-2}=0.0625$ can be written as ${\log }_4^{}0.0625=-2$ in logarithmic form.

Explanation of Solution

Given information:

The expression is $4^{-2}=0.0625$ .

Calculation:

Consider the given expression.

  $4^{-2}=0.0625$

Arrange the expression.

  $\begin{array}{c}{4}^{-2}=0.0625\\ {\log }_4^{}0.0625=-2\left\{\begin{array}{r}\text{Property}\\ x=a^y\\ {\log }_a^{}x=y\end{array}\right\}\end{array}$

Therefore, the expression $4^{-2}=0.0625$ can be written as ${\log }_4^{}0.0625=-2$ in logarithmic form.