Question:
If the fourth term in the expansion of $\left(\mathrm{x}+\mathrm{x}^{\log _{2} \mathrm{x}}\right)^{7}$ is 4480 , then the value of $x$ where $x \in N$ is equal to:
Correct Option: 1
Solution:
${ }^{7} \mathrm{C}_{3} \mathrm{x}^{4} \mathrm{x}\left({ }^{3 \log _{2}^{2}}\right)=4480$
$\Rightarrow x\left(4+3 \log _{2}^{2}\right)=2^{7}$
$\Rightarrow \quad(4+3 \mathrm{t}) \mathrm{t}=7 ; \mathrm{t}=\log _{2}^{\mathrm{x}}$
$\Rightarrow \mathrm{t}=1, \frac{-7}{3} \Rightarrow \mathrm{x}=2$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.