Chapter 8.2, Problem 24PPS

To determine

To find: the solution of the given inequality.

Answer to Problem 24PPS

The solution of the inequality is $a\le -4$ .

Explanation of Solution

Given information:

The given inequality is $625\ge 5^{a+8}$

If the base of any two exponential functions are equal then the exponent of the function are also equal. If $a^x=a^y$ then $x=y$ .

The inequality $625\ge 5^{a+8}$ can be written as $625=5^{a+8}$ .

Solve the inequality.

  $\begin{array}{c}{5}^4=5^{a+8}\\ 4\ge a+8\\ a\le 4-8\\ \le -4\end{array}$

Therefore, the solution of the inequality is $a\le -4$ .