Chapter 9.1, Problem 59SR

To determine

To find: The solution for each of the equation or inequality round to the nearest ten thousand.

Answer to Problem 59SR

The required solution is $p\le 1.9803$ .

Explanation of Solution

Given:

The given function is $7^{p+2}\le {13}^{5-p}$ .

Calculation:

Consider the given equation or inequality is,

  $7^{p+2}\le {13}^{5-p}$

Solve the above equation by taking algorithm of both the sides.

  $\begin{array}{l}\log 7^{p+2}\le \log {13}^{5-p}\\ \left(p+2\right)\log 7\le \left(5-p\right)\log 13\\ p\log 7+p\log 13\le 5\log 13-2\log 7\\ p\le \frac{5\log 13-2\log 7}{\log 7+\log 13}\end{array}$

Solve further as,

  $\begin{array}{l}p\le \frac{5.5697165-1.690196}{1.959041392}\\ p\le 1.9803\end{array}$