Algebra-1

Question Analysis
This question tests the student's ability to solve exponential equations by rewriting both sides with the same base. The key is to recognize that both 27 and 9 can be expressed as powers of 3.

Key Concept Explanation
The core principle is that if two exponential expressions with the same base are equal, their exponents must be equal. This is because the exponential function is injective (one-to-one).

Step-by-step Solution
1. Rewrite 27 and 9 as powers of 3: and .
2. Substitute these into the equation: .
3. Simplify the exponents: