Q 91. - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation. 

${\log }_{x}4=2$

Step-by-Step Solution

Answer

The solution to the equation, ${\log }_{x}4=2$is, $x=2$.

Step 1. Given Information

The given equation to be solved is ${\log }_{x}4=2$.

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 ${\log }_{x}4=2$.

Use rule of change from logarithm to exponents:

$$\begin{gathered} {\log }_{x}4=2 \\ {x}^2=4 \\ x=2 \end{gathered}$$

The solution to the given equation is, $x=2$.