Chapter 8.7, Problem 82S

To determine

To find: The value of given variable.

Answer to Problem 82S

The value of given variable is $p=-3$ .

Explanation of Solution

Given information:

The equation is ${32}^{2p}={216}^{p-1}$ .

Calculation:

Consider the equation.

  $\begin{array}{l}{32}^{2p}={216}^{p-1}\\ 6^{4p}=6^{3p-3}\\ {\log }_6{6}^{4p}={\log }_6{6}^{3p-3}\\ 4p{\log }_{6}6=\left(3p-3\right){\log }_{6}6\\ 4p=3p-3\\ p=-3\end{array}$