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
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
A. 1
B. `log_(e)10`
C. `10`
D. `x` does not exist
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1 Answers
Correct Answer - C
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`
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Answered