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Property 6

Solve the fol...

Question

Solve the following equation:
$x^{{log}_{\sqrt{x}} (x - 2)} = 9$

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Solution

$_{x} {l o g}_{\sqrt{x}} (x - 2) = 9 \Rightarrow {(x - 2)}^{l o g x} \sqrt{x} = 9 \Rightarrow {(x - 2)}^{2} = 9 \Rightarrow x - 2 = 3$

Therefore, $x - 2 > 0$
$\Rightarrow x = 5$

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