Chapter 11.10, Problem 40E

To determine

To find: The solution for the given equation.

Answer to Problem 40E

The solution of the given equation is $n=\frac{3}{2}$ .

Explanation of Solution

Given:

The given equation is $7^{\left(\frac{7}{5}\right)n}\cdot 7^{\left(\frac{3}{5}\right)n}=343$ .

Calculation:

Consider the given equation is,

  $7^{\left(\frac{7}{5}\right)n}\cdot 7^{\left(\frac{3}{5}\right)n}=343$

Then, the solution is,

  $\begin{array}{l}{7}^{\left(\frac{7}{5}\right)n}\cdot 7^{\left(\frac{3}{5}\right)n}=343\\ 7^{\left(\frac{7}{5}+\frac{3}{5}\right)n}=343\\ 7^{2n}=7^3\\ 2n=3\end{array}$

Solve further as,

  $n=\frac{3}{2}$