Algebra-2

Question Analysis
This problem tests the ability to solve logarithmic equations involving quadratic expressions and to find all valid solutions.

Key Concept Explanation
To solve the equation, we first convert it to its exponential form and then solve the resulting quadratic equation. We must also verify that the solutions satisfy the domain of the logarithmic function.

Step-by-step Solution
1. Convert to exponential form: .
2. Rearrange the equation: .
3. Solve the quadratic equation using the quadratic formula: .
4. Simplify the solutions: and .
5. The argument of the logarithm must be positive:

Click "Show Answer" to reveal the answer and analysis