Chapter 5, Problem 7CT

To determine

The solution of the equation ${\log }_{5}x=4$ .

Answer to Problem 7CT

Solution:

The solution of the equation ${\log }_{5}x=4$ is $x=625$ .

Explanation of Solution

Given information:

The equation is ${\log }_{5}x=4$ .

As $y={\log }_{a}x$ and $x=a^y,$ where $a>0$ and $a\ne 1,$ are equivalent,

  $\Rightarrow x=5^4$

  $\Rightarrow x=625$

Therefore, the solution of the equation ${\log }_{5}x=4$ is $x=625$ .