Question

If the third term in the expansion of $[x+x^{log}{10}^x{]}^{5}is{10}^6$ then x must be

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$T_3=T_{2+1}{=}^5{C}_2{x}^{5-2}(x^{log}{10}^x{)}^2$
$=10x^3{x}^{2log}{10}^x=10x^{(}3+2log{10}^x)={10}^6(given)\Rightarrow x^{3+2log}{10}^x={10}^5$
x=10 will satisfy this.