Question

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

• A. $10$
• B. $11$
• C. $12$
• D. $Noneofthese$

Answer 1

The correct option is A $10$

The third term of the expression will be,

${}^5{C}_2{x}^3(x^{{\log }_{x}10}{)}^2=10,00,000$

or, $x^3.\left({10}^2\right)=10,00,00$ [ Since ${}^5{C}_2=10$]

or, $x^3=1000$

or, $x=10$.