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 :
Correct Option: 1
Solution:
${ }^{7} \mathrm{C}_{3} \mathrm{x}^{4} \mathrm{x}^{\left(3 \log _{2}^{\mathrm{x}}\right)}=4480$
$\Rightarrow \mathrm{x}^{\left(4+3 \log _{2}^{\mathrm{x}}\right)}=2^{7}$
$\Rightarrow(4+3 \mathrm{t}) \mathrm{t}=7 ; \mathrm{t}=\log _{2}^{\mathrm{x}}$
$\Rightarrow \mathrm{t}=1, \frac{-7}{3} \Rightarrow \mathrm{x}=2$
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