Chapter 11.10, Problem 38E

To determine

To find: The solution for the given equation.

Answer to Problem 38E

The solution of the given equation is $n=2$ .

Explanation of Solution

Given:

The given equation is $6^{\left(\frac{1}{2}\right)n}\cdot 6^{\left(\frac{1}{2}\right)n}=36$ .

Calculation:

Consider the given equation is,

  $6^{\left(\frac{1}{2}\right)n}\cdot 6^{\left(\frac{1}{2}\right)n}=36$

Then, the solution is,

  $\begin{array}{l}{6}^{\left(\frac{1}{2}\right)n}\cdot 6^{\left(\frac{1}{2}\right)n}=36\\ 6^{\left(\frac{1}{2}+\frac{1}{2}\right)n}\cdot =36\\ 6^n=6^2\\ n=2\end{array}$