If the fourth term in the expansion of

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:

  1. (1) 2

  2. (2) 4

  3. (3) 3

  4. (4) 1


Correct Option: 1

Solution:

${ }^{7} \mathrm{C}_{3} \mathrm{x}^{4} \mathrm{x}\left({ }^{3 \log _{2}^{2}}\right)=4480$

$\Rightarrow x\left(4+3 \log _{2}^{2}\right)=2^{7}$

$\Rightarrow \quad(4+3 \mathrm{t}) \mathrm{t}=7 ; \mathrm{t}=\log _{2}^{\mathrm{x}}$

$\Rightarrow \mathrm{t}=1, \frac{-7}{3} \Rightarrow \mathrm{x}=2$

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