JEE MainMathematicsModerateLogarithm

The equation
$x^{\frac{3}{4}{(\log_{2}x)}^{2} + \log_{2}x - \frac{5}{4}} = \sqrt{2}$
has

Show answer and solution

Taking logarithm

(\frac{3}{4}y^{2} + y - \frac{5}{4})y = \frac{1}{2}

Where

y = \log_{2}x

(y - 1)(3y + 1)(y + 2) = 0

\Rightarrow \log_{2}x = 1, - \frac{1}{3}, - 2

\Rightarrow x = 2,2^{- 1/3},2^{- 2}

Source: Grass-G / M-16 Mathematics Paper 25 Nov First.docx

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