Chapter 8.4, Problem 38HP

To determine

The solution of the error.

Answer to Problem 38HP

Ryan was correct.

Explanation of Solution

Given information:

Ryan and Heather are solving ${\log }_{3}x\ge -3$ . Is either of them correct? Explain your reasoning?

  

Calculation:

Find the given inequality by the property of inequality for logarithmic functions is as shown below:

  $\begin{array}{l}{\log }_{3}x\ge -3\text{ [The original equation]}\\ x\ge 3^{-3}\text{ [Property of inequality for logarithmic functions]}\\ x\ge \frac{1}{3^3}\text{ [Simplify]}\\ x\ge \frac{1}{27}\end{array}$

Therefore, Ryan was correct. Heather did not need to switch the inequality symbol when raising to a negative power.