Chapter 8, Problem 31SGR

To determine

To solve: The equation ${\log }_{16}x=\frac{3}{4}$

Answer to Problem 31SGR

The solution ${\log }_{16}x=\frac{3}{4}$ of the equation is $x=64$ .

Explanation of Solution

Given:

The equation is ${\log }_{16}x=\frac{3}{4}$ .

Calculation:

Simplify the equation ${\log }_{16}x=\frac{3}{4}$ as follows.

  $\begin{array}{c}{\log }_{16}x=\frac{3}{4}\\ {16}^{3/2}=x\\ x=64\end{array}$

Therefore, the solution ${\log }_{16}x=\frac{3}{4}$ of the equation is $x=64$ .