Chapter 8.4, Problem 1ACYP

To determine

The solution of inequality.

Answer to Problem 1ACYP

  $3^3\text{ or 27}$ .

Explanation of Solution

Given information:

Solve the inequality:

  ${\log }_{9}x=\frac{3}{2}$

Calculation:

The given logarithm equation is ${\log }_{9}x=\frac{3}{2}$ .

To solve the inequality logarithmic equation by using the defination of a logarithm are as shown below:

  $\begin{array}{l}{\log }_{9}x=\frac{3}{2}\text{ {The original equation}}\\ x=9^{\frac{3}{2}}\text{ {Defination of logarithm} }\\ $ x={(3^2)}^{\frac{3}{2}}{\text{ {9=3}}^2\text{}}$x=3^3\text{ or 27}\end{array}$

Thus, the solution of the inequality is $3^3\text{ or 27}$ .