Chapter 8.6, Problem 23PPS

To determine

To find: The value of given variable.

Answer to Problem 23PPS

The value of given variable is $x=1.77$ .

Explanation of Solution

Given information:

The equation is $8^x=40$ .

Calculation:

Consider the equation.

  $\begin{array}{l}{8}^x=40\\ {\log }_8{8}^x={\log }_{8}40\\ x{\log }_{8}8={\log }_{8}40\\ x=\frac{{\log }_{8}40}{{\log }_{8}8}\\ x=\frac{1.6}{0.9}\\ x=1.77\end{array}$