Chapter 11.4, Problem 33E

To determine

The solution of the expression.

Answer to Problem 33E

  $x=\frac{1}{3}$ .

Explanation of Solution

Given information:

Evaluate the expression:

  ${\log }_{125}5$

Calculation:

The given expression is ${\log }_{125}5$ .

Let $x={\log }_{125}5$

By the defination of the logarithm

  ${125}^x=5$

Write $125$ as a $5^3$ :

  ${(5^3)}^x=5$

By power of power rule:

  $5^3{}^x=5$

If $a^u=a^v$ then $u=v$ ,

  $\begin{array}{l}3x=1\\ x=\frac{1}{3}\end{array}$

Thus, the solution is $x=\frac{1}{3}$ .