Chapter 8.2, Problem 25PPS

To determine

To find: the solution of the given inequality.

Answer to Problem 25PPS

The solution of the inequality is $b>\frac{1}{5}$ .

Explanation of Solution

Given information:

The given inequality is ${10}^{5b+2}>1000$

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 $x=y$ .

Consider the inequality.

  ${10}^{5b+2}>1000$ .

Solve the inequality.

  $\begin{array}{c}{10}^{5b+2}>1000\\ {10}^{5b+2}>{10}^3\\ 5b>3-2\\ b>\frac{1}{5}\end{array}$

Therefore, the solution of the inequality is $b>\frac{1}{5}$ .