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Third term in expression of (x + x^(log(...

Third term in expression of `(x + x^(log_(10)x))^(5)` is `10^(6)` than possible value of `x` are

A

`1`

B

`10`

C

`10^(-5//2)`

D

`10^(6)`

Text Solution

Verified by Experts

The correct Answer is:
B, C
`T_(3) = .^(5)C_(2)x^(3)(x^(log_(10)x))^(2) = 10.x^(3+2log_(10)x)=10^(6)`
`rArr x^(3+2log_(10)x) = 10^(5)`
taking `log` on both sides
`(3 + 2log_(10)x)log_(10)x=5`
`rArr log_(10)x = 1` or `-(5)/(2)`
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