# The sixth term in the expansion of ( 1/x^8/3 + x^2 log x )^8 (where base is 10) is 5600. the number of values of x is

Solution:   We have ,

$(\frac{1}{x^\frac{8}{3}}+x^{2}\log_{10}x)^{8}$

$\Rightarrow$         $^8c_5\cdot \frac{1}{x^{8}}\cdot x^{10}(\log_{10}x)^{5}=5600$

$\Rightarrow$                         $(\log_{10}x)^{5}=\frac{5600}{56x^{2}}=(\frac{10}{x})^{2}$

$\Rightarrow$                                  $x=10.$

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