Chapter 8.6, Problem 43PPS

To determine

To find: The value of given variable.

Answer to Problem 43PPS

The value of given variable is $n=-0.065$ .

Explanation of Solution

Given information:

The equation is $4^{n+2}=14.5$ .

Calculation:

Consider the equation.

  $\begin{array}{l}{4}^{n+2}=14.5\\ {\log }_4{4}^{n+2}={\log }_{4}14.5\\ \left(n+2\right){\log }_{4}4={\log }_{4}14.5\\ n+2={\log }_{4}14.5\\ n+2=\frac{\log 14.5}{\log 4}\\ n+2=\frac{1.161}{0.6}\\ n+2=1.935\\ n=1.935-2\\ n=-0.065\end{array}$