Question

If 2^x · 3^y = 288, then the value of y is ______.

Options

• 1

• 2

• –2

• –1

Answer 1

If 2^x · 3^y = 288, then the value of y is 2.

Explanation:

Given the equation: 2^x × 3^y = 288

Step 1: Factorize 288 into prime factors.

288 = 2⁵ × 3²

Step 2: Equate the powers of the prime bases on both sides since the bases are the same.

This means x = 5 and y = 2.

Therefore, the value of y is 2.