JEE MainMathematicsEasyLogarithm

If $\frac{logx}{2} = \frac{logy}{3} = \frac{logz}{5},$ then
$x^{2} =$

Show answer and solution

\frac{logx}{2} = \frac{logy}{3} = \frac{logz}{5}

then

x^{1/2} = K

y^{1/3} = K,z^{1/5} = K

\Rightarrow x = K^{2},y = K^{3},z = K^{5} \Rightarrow x^{2} = K^{4}

\sqrt{yz} = \sqrt{K^{8}} = K^{4} \Rightarrow x^{2} = \sqrt{yz}

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

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