Chapter 8.6, Problem 81STP

To determine

To find: The value of the equation.

Answer to Problem 81STP

The value of the equation is $x=2$ .

Explanation of Solution

Given information:

The given equation is ${\log }_{4}x=\frac{1}{2}$ .

Calculation:

Consider the equation:

  ${\log }_{4}x=\frac{1}{2}$

Formula is given as.

  $\begin{array}{l}{\log }_{a}b=c\\ {\log }_{a}b=a^c\end{array}$

Where, $a=4$ , $b=x$ and $c=\frac{1}{2}$

Now,

  $\begin{array}{c}{\log }_{4}x=\frac{1}{2}\\ x=4^{\frac{1}{2}}\\ x=2\end{array}$

Therefore, the value of the equation is $x=2$ .