Question

The value of x in the expression $(x+x^{lo{g}_{10}x}{)}^5$ if the third term in the expansion is ${10}^6$:

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

Answer 1

The correct option is A

10

${10}^6=T_{2+1}={}^5{C}_2\left(x{)}^{5-2}\right(x^{{\log }_{10}x}{)}^2$

or ${10}^5=x^3(x^{{\log }_{10}x}{)}^2$

If x = 10 in (i),then

${10}^5=\left(10{)}^3\right({10}^{{\log }_{10}10}{)}^2={10}^5$ (True)