Question

If the fourth term in the expansion of ${\left(x+x^{{\log }_{2}x}\right)}^7$ is 4480, then the value of $x$ where $x\in N$ is equal to :

• A. 2
• B. 4
• C. 3
• D. 1

Answer 1

Answer: (A)

${}^7{C}_3{x}^4{x}^{\left(3{\log }_2^x\right)}=4480$
$\Rightarrow x^{\left(4+3{\log }_2^x\right)}=2^7$
$\Rightarrow (4+3t)t=7;t={\log }_2^x$
$\Rightarrow t=1,\frac{-7}{3}\Rightarrow x=2$