If the 6^{th} term in the expansion of the bi | vedclass

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(C) The general term $T_{r+1}$ in the expansion of $(a+b)^n$ is given by $^nC_r a^{n-r} b^r$. For the $6^{th}$ term,$r = 5$ and $n = 8$. $T_6 = ^8C_5

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$10$

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(C) The general term $T_{r+1}$ in the expansion of $(a+b)^n$ is given by $^nC_r a^{n-r} b^r$. For the $6^{th}$ term,$r = 5$ and $n = 8$. $T_6 = ^8C_5 \left( \frac{1}{x^{8/3}} \right)^{8-5} (x^2 \log_{10} x)^5 = 5600$. $T_6 = ^8C_5 (x^{-8/3})^3 (x^{10} (\log_{10} x)^5) = 5600$. $T_6 = 56 \cdot x^{-8} \cdot x^{10} \cdot (\log_{10} x)^5 = 5600$. $56 \cdot x^2 \cdot (\log_{10} x)^5 = 5600$. $x^2 (\log_{10} x)^5 = 100$. If $x = 10$,then $10^2 (\log_{10} 10)^5 = 100 \cdot 1^5 = 100$. Thus,$x = 10$ satisfies the equation.

If the $6^{th}$ term in the expansion of the binomial $\left[ \frac{1}{x^{8/3}} + x^2 \log_{10} x \right]^8$ is $5600$,then $x$ equals to

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