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  • The sixth term in the expansion of <img alt="\left(\frac{1}{x^{8 / 3}}+x^2 \log _{10} x\right)^8"

The sixth term in the expansion of \left(\frac{1}{x^{8 / 3}}+x^2 \log _{10} x\right)^8 is 5600 when x is equal to

Option: 1

10


Option: 2

\log _{\mathrm{e}} 10


Option: 3

1


Option: 4

none of these


Answers (1)

best_answer

T_6={ }^8 C_5\left(\frac{1}{x^{8 / 3}}\right)^3\left(x^2 \log _{10} x\right)^5 \Rightarrow 56 x^2\left(\log _{10} x\right)^5=5600

\Rightarrow x^2\left(\log _{10} x\right)^5=100, obviously x = 10 satisfies the above equation.

Hence (A) is the correct answer.

 

Posted by

chirag

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