Chapter 11.3, Problem 40SR

To determine

To find: The solution.

Answer to Problem 40SR

The solution is $1000$ .

Explanation of Solution

Given:

The given equation is,

  ${\log }_{\frac{1}{10}}x=-3$

Calculation:

The equation is simplified as,

  $\begin{array}{c}{\log }_{\frac{1}{10}}x=-3\\ x={\left(\frac{1}{10}\right)}^{-3}\\ ={10}^3\\ =1000\end{array}$

Therefore, the solution is $1000$ .