Question

Find the values of x, y and z from the following: 

2^x · 3^y · 5^z = 24000

Answer 1

Given: 2^x · 3^y · 5^z = 24000

Step-wise calculation:

1. Prime factorize 24000:

24000 = 24 × 1000

24000 = (2³ × 3) × (10³)

24000 = 2³ × 3¹ × (2 × 5)³

24000 = 2³ × 3¹ × 2³ × 5³

24000 = 2⁶ × 3¹ × 5³

2. Compare exponents of the prime factorization:

2^x = 2⁶

⇒ x = 6 

3^y = 3¹

⇒ y = 1 

5^z = 5³

⇒ z = 3