Chapter 8.5, Problem 49PPS

To determine

To find: The value of each of the equation.

Answer to Problem 49PPS

The solution of the equation exists for the value $p=12$ .

Explanation of Solution

Given:

The given equation is ${\log }_{7}64+{\log }_7\frac{8}{3}+{\log }_{7}2={\log }_{7}4p$ .

Calculation:

Consider the given equation is,

  ${\log }_{7}64+{\log }_7\frac{8}{3}+{\log }_{7}2={\log }_{7}4p$

Solve the above equation as,

  $\begin{array}{l}{\log }_7\frac{64}{\frac{8}{3}}+{\log }_{7}2={\log }_{7}4p\\ {\log }_7\frac{64\cdot 2}{\frac{8}{3}}={\log }_{7}4p\\ 48=4p\\ p=12\end{array}$

Thus, the solution of the equation exists for the value $p=12$ .