Linear Inequalities In One Variable

We are given the inequality: We will first simplify the terms to solve for .

Step 1: Expressing logarithmic terms
We start by simplifying the first term, . Using the logarithmic property , we have: The second term can be simplified using the change of base formula . Thus, we get:

Step 2: Substituting into the inequality
Now, substitute these expressions into the original inequality: Let . Substituting into the inequality: This simplifies to: Now, solve for (and thus ) by considering this inequality. After solving the inequality, we find that lies in the range .

Answer: