Question

If 2^x 5^y = 500, then (x+y) is
(A) multiple of 2
(B) multiple of 3
(C) multiple of 5
(D) multiple of 10​

Answer 1

Answer:

$= > {2}^{x} \times {5}^{y} = 500$

$= > 500 = 2 \times 2 \times 5 \times 5 \times 5 = {2}^{2} \times {5}^{3}$

$i.e. \: x = 2 \: and \: y = 3$

$so \: = > x + y = 2 + 3 = 5$

$which \: \: is \: \: a \: \: multiple \: \: of \: \: 5$

Hence , answer is (C)

Hope this answer helps you ^_^ !