Chapter 8.4, Problem 3ACYP

To determine

The solution of logarithmic inequality.

Answer to Problem 3ACYP

  $2^3\text{ or 8}$ .

Explanation of Solution

Given information:

Solve the inequality:

  ${\log }_{4}x\ge 3$

Calculation:

The given logarithm inequality is ${\log }_{4}x\ge 3$ .

To solve the inequality logarithmic equation by using property of inequality for logarithmic function:

  $\begin{array}{l}{\log }_{4}x\ge 3\text{ {The original equation}}\\ x\ge 4^3\text{ {By using property }{\log }_{b}x>y,\text{then }x>b^y\text{} }\\ x\ge 64\end{array}$

Thus, the solution of the inequality is $x\ge 64$ .