Q 95. - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation. 

${\log }_{4}64=x$

Step-by-Step Solution

Answer

The solution to the equation, ${\log }_{4}64=x$is, $x=3$.

Step 1. Given Information

The given equation to be solved is ${\log }_{4}64=x$.

Step 2. Formula used

Rule of change from logarithm to exponents: 

${\log }_{a}b=y\Rightarrow a^y=b$

Step 3. Finding Solution

The given equation is ${\log }_{4}64=x$.

Use rule of change from logarithm to exponents: 

$$\begin{gathered} {\log }_{4}64=x \\ {4}^x=64 \\ {\left(4\right)}^x={\left(4\right)}^{3}x=3 \end{gathered}$$

The solution to the given equation is, $x=3$.