If the third term in the expansion of $[x + x^{l o g} 10^{x}]^{5} i s 10^{6}$ then x must be

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Solution

The correct option is C
$T_{3} = T_{2 + 1} =^{5} C_{2} x^{5 - 2} (x^{l o g} 10^{x})^{2}$
$= 10 x^{3} x^{2 l o g} 10^{x} = 10 x^{(} 3 + 2 l o g 10^{x}) = 10^{6} (g i v e n) \Rightarrow x^{3 + 2 l o g} 10^{x} = 10^{5}$
x=10 will satisfy this.

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