The value of x in the expression ${[x + x^{l o g_{10} (x)}]}^{5}$ ,if the third term in the expansion is 10,00,000

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Solution

The correct option is A 10
$T_{3} =^{5} C_{2} . x^{2} (x^{l o g 10 x}) = 10^{6}$
${put}^{5} C_{2} = 10 [∵ l o g_{10} 10 = 1]$
$I f x = 10, t h e n 10^{3} {.10}^{2.1} = 10^{5}$ is satisfied
Hence x = 10

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