Question

x^x^1/2=x^1/2^x find the value of X

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Answer 1

${x}^{ \sqrt{x} } = { \sqrt{x} }^{x}$

taking log both side,

formula used : log aⁿ = n× log a

$\sqrt{x} \times log(x) = x \times log( \sqrt{x} )$

$\sqrt{x} \times log(x) = x \times \frac{1}{2} log( {x} )$

x= 2√x

x²= 4x (as x≠0)

x= 4

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