Question

The value of x in the expression $[x+x^{lo{g}_{10}\left(x\right)}{]}^5$, if the third term in the expansion is 10,00,000

• A. 10
• B. 11
• C. 12
• D. None of these

Answer 1

The correct option is A

10

$T_3$ = ${}^5{C}_2$. $x^2$$(x^{lo{g}_{10}x}{)}^3$ = ${10}^6$

Put ${}^5{C}_2$ = 10 [ ∵$lo{g}_{10}10=1$].

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

Hence x = 10.