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If the third term in the expansion of ${[\frac{1}{x} + x^{\log_{10} x}]}^{5}$
$x > 1,$ is $1000,$ then $x$ equals

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Correct option is D

T3=5C21x3xlog10⁡x2=10x2log10⁡x−3As T3=1000 we get(2a−3)a=2 where a=log10⁡x⇒2a2−3a−2=0⇒(2a+1)(a−2)=0 As x>1,a=log10⁡x>0, thus, a=2⇒log10⁡x=2⇒x=100

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If the third term in the expansion of 1x+xlog10⁡x5x>1, is 1000, then xequals

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If the third term in the expansion of ${[\frac{1}{x} + x^{\log_{10} x}]}^{5}$
$x > 1,$ is $1000,$ then $x$ equals