The value of x in the expression [x+xlog10(x)]5, if the third term in the expa

Question -

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

Options:

A . 10

B . 11

C . 12

D . None of these

Answer: Option A
:
A

$T_{3}$ = $^{5} C_{2}$ . $x^{2}$ $(x^{l o g_{10} x})^{3}$ = $10^{6}$

Put $^{5} C_{2}$ = 10 [ ∵ $l o g_{10} 10 = 1$ ].

If x = 10, then $10^{3}$ . $10^{2.1}$ = $10^{5}$ is satisfied.

Hence x = 10.

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