Chapter 7.6, Problem 51PPS

To determine

To find: The value of given variable.

Answer to Problem 51PPS

The value of given variable is $p\le 2.9437$ .

Explanation of Solution

Given information:

The equation is $6^p\le {13}^{5-p}$ .

Calculation:

Consider the equation.

  $\begin{array}{l}{6}^p\le {13}^{5-p}\\ \log 6^p\le \log {13}^{5-p}\\ p\log 6\le \left(5-p\right)\log 13\\ p\log 6\le 5\log 13-p\log 13\\ p\log 6+p\log 13\le 5\log 13\\ \frac{p\left(\log 6+\log 13\right)}{\log 6+\log 13}\le \frac{5\log 13}{\log 6+\log 13}\\ p\le \frac{5\log 13}{\log 6+\log 13}\\ p\le 2.9437\end{array}$