Chapter 8, Problem 18SGR

To determine

To find: The solution of the equation for the inequality.

Answer to Problem 18SGR

The solution of the equation is $\frac{-3}{2}$ .

Explanation of Solution

Given:

The given function is ${16}^x=\frac{1}{64}$ .

Calculation:

Consider the given equation is,

  ${16}^x=\frac{1}{64}$

Solve the above equation for the value of $x$ .

  $\begin{array}{l}{\left(4^2\right)}^x=\frac{1}{4^3}\\ 4^{2x}=4^{-3}\\ 2x=-3\\ x=\frac{-3}{2}\end{array}$