x^log_3 x=9 (log_3 x)^2=log _3 3^2 (log _3 x)^2=2 log_3 x=±√(2) x=3^√(2),3^ √(2) ...

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Property 6

Evaluate xl...

Question

Evaluate $x^{{log}_{3} x} = 9$

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Solution

$x^{{log}_{3} x} = 9$
$({log}_{3} x)^{2} = {log}_{3} 3^{2}$
$({log}_{3} x)^{2} = 2$
${log}_{3} x = \pm \sqrt{2}$
$x = 3^{\sqrt{2}}, 3^{- \sqrt{2}}$

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