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if x in N, then the value of x satisfyin...

if `x in N`, then the value of x satisfying the equation `5^x*(8^(x-1))^(1/x)=500` is divisible by

A

2

B

4

C

3

D

5

Text Solution

Verified by Experts

The correct Answer is:
C
`5^(x).root(x)(8^(x-1))=500, x in N`
`rArr 5^(x).8^((x-1)/(x))=500`
`rArr 5^(x).2^((3(x-1))/(x))=5^(3).2^(2)`
`rArr x=3` and `(3(x-1))/(x)=2`
`rArr x=3`
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