Q. The value of $x$ in the expansion ${\lbrack x + x^{\log_{10}x}\rbrack}^{5}$, if the third term in the expansion is 1000000, is
A) 10
B) 11
C) 12
D) None of these
Explanation
(a)
Given expression is $\left( x + x^{\log 10^{x}} \right)^{5}$
$\therefore T_{3} = \ ^{5}C_{2} \bullet x^{3}\left( x^{\log 10^{x}} \right)^{2} = 10^{6}$ (given)
Put$\ x = 10$, then $10^{4}.10^{2} = 10^{6}$ is satisfied. Hence, $x = 10$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.