Chapter 13.3, Problem 71STP

To determine

To find: Solve each equation.

Answer to Problem 71STP

  $x\approx 2.5841$

Explanation of Solution

Given information:

  $5^x=64$

Given

  $5^x=64$

Using the logarithm functions

We get

  $\begin{array}{l}{5}^x=64\\ \Rightarrow \log \left(5^x\right)=\log \left(64\right)\\ \Rightarrow x\log \left(5\right)=\log \left(64\right)\\ \Rightarrow \frac{x\log \left(5\right)}{\log \left(5\right)}=\frac{\log \left(64\right)}{\log \left(5\right)}\\ \Rightarrow x=\frac{\log \left(64\right)}{\log \left(5\right)}\\ \Rightarrow x=\frac{1.8061}{0.699}\\ \Rightarrow x\approx 2.5841\end{array}$

Therefore,

  $x\approx 2.5841$