"If the fourth term in the expansion of ${(x + {x^{{{\log }_2}x}})^7}$ is 4480, then the value of x where x$\in$N is equal to :"

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Accepted Answer

"T₄ = ${}^7{C_3}{x^4}{({x^{{{\log }_2}x}})^3} = 4480$

$\Rightarrow 35{x^4}{({x^{{{\log }_2}x}})^3} = 4480$

$\Rightarrow {x^4}{({x^{{{\log }_2}x}})^3} = 128$

take log w.r.t. base 2 we get,

$4{\log _2}x + 3{\log _2}({x^{{{\log }_2}x}}) = {\log _2}128$

Let ${\log _2}x = y$

$4y + 3{y^2} = 7$

$\Rightarrow y = 1,{{ - 7} \over 3}$

$\Rightarrow {\log _2}x = 1,{{ - 7} \over 3}$

$\Rightarrow$ $x = 2,x = {2^{ - 7/3}}$"

If the fourth term in the expansion of ${(x + {x^{{{\log }_2}x}})^7}$ is 4480, then the value of x where x$\in$N is equal to :

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If the fourth term in the expansion of ${(x + {x^{{{\log }_2}x}})^7}$ is 4480, then the value of x where x$\in$N is equal to :

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