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  4. If the fourth term in the expansion of ( x + x log 2 x )7 is 4480, then the value of x where x ∈ N is equal to :

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Q. 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 :

JEE MainJEE Main 2021Binomial Theorem

Solution:

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