Chapter 11.5, Problem 64E

To determine

To Find: The expression $y$ in terms of p, q and r.

Answer to Problem 64E

The required expression is. $y=\frac{p}{q}r$ .

Explanation of Solution

Given:

The given expression as,

  ${\log }_{a}y={\log }_{a}p-{\log }_{a}q+{\log }_{a}r$

Calculation:

Consider the expression is,

  ${\log }_{a}y={\log }_{a}p-{\log }_{a}q+{\log }_{a}r$

Then,

  $\begin{array}{l}{\log }_{a}y={\log }_{a}p-{\log }_{a}q+{\log }_{a}r\\ {\log }_{a}y={\log }_a\left(\frac{p}{q}\right)+{\log }_{a}r\\ {\log }_{a}y={\log }_a\left(\frac{p}{q}\right)r\\ y=\frac{p}{q}r\end{array}$