PSAT Math Multiple-Choice Question 1: Answer and Explanation

Question: 1

If 3⁴ = 9^x, what is the value of x?

• A. 2
• B. 3
• C. 4
• D. 5

Correct Answer: A

Explanation:

A

The question asks for the value of a variable in an equation involving exponents. When given equivalent exponent terms with different bases, rewrite the exponent terms using the same base. Rewrite 3⁴ as 3 × 3 × 3 × 3 = 9 × 9. Therefore, 3⁴ = 9² and x = 2. An alternative solution is to calculate 3⁴ = 81. If 3⁴ = 9^x, then 81 = 9^x, and x = 2. The correct answer is (A).