Question

If 2400 = 2^x x 3^y x 5^z, find the numerical value of x, y, z. Find the value of 2^-x x 3^y x 5^z as fraction.

Answer 1

2400 = 2^x x 3^y x 5^z
2400 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5
∴ 2^x x 3^y x 5^z = 2⁵ x 3¹ x 5²
⇒ x = 5, y = 1, z = 2
∴ 2^-x x 3^y x 5^z = 2^-5 x 3¹ x 5²

= `(1)/(32) xx 3 xx 25`

= `(75)/(32)`.