Question

Find the value of x and y from the following:

3^x · 5^y = 675

Answer 1

Given: 3^x · 5^y = 675

Step-wise calculation:

1. Factorize 675 into prime factors: 

675 = 3³ × 5²

2. Comparing both sides, since the bases are the same: 

3^x = 3³ 

⇒ x = 3

5^y = 5² 

⇒ y = 2

The values are x = 3, y = 2.

Hence, 3³ × 5² = 675 which satisfies the given equation.