If the 6th term in the expansion of`(1/(x^(8/3))+x^2(log)_(10)x)^8` is 5600, then `x` equals `1` b. `(log)_e 10` c. `10` d. `x` does not exist

Options

A. 1
B. `log_(e)10`
C. `10`
D. `x` does not exist

Answer

C

Explanation

It is given that `6^(th)` term in expansion of
`((1)/(x^(8//3))+x^(2)log_(10)x)^(6)` is `5600`, therefore
`.^(9)C_(5)(x^(2)log_(10)x)^(5)((1)/(x^(8//3)))^(3) = 5600`
or `56x^(10)(log_(10)x)^(5) (1)/(x^(8)) = 5600`
or `x^(2)(log_(10)x)^(5) = 100`
or `x^(2)(log_(10)x)^(5) = 10^(2)(log_(10)10)^(5)`
or `x = 10`