If the fourth term in the expansion of (x + x ^ _ 2 x ) ^ 7 is...

Given ${\left(x + {x}^{\log_{2}x}\right)}^{7} .$

The general term in the expansion of ${\left(x + {x}^{\log_{2}x}\right)}^{7}$ is $Cr 7 {x}^{r}{\left({x}^{\log_{2}x}\right)}^{7 - r} .$

Then, ${T}_{4} =$$C3 7 {x}^{4}{\left({x}^{\log_{2}x}\right)}^{3} = 4480$

$⇒ \dfrac{7 \cdot 6 \cdot 5}{3 \cdot 2 \cdot 1}{x}^{4 + \log_{2}x} = 4480$

$⇒ {x}^{\left(4 + 3\log_{2}x\right)} = 128$

$⇒ {x}^{\left(4 + 3\log_{2}x\right)} = {2}^{7}$

Now, from the option only at $x = 2$, $LHS = RHS .$