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Solve the fol...

Question

Solve the following equations.
$l o g \sqrt{x - 3} + l o g \sqrt{2 x - 1} = l o g \sqrt{3 x + 3} .$

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Solution

$log \sqrt{x - 3} \sqrt{2 x - 1} = log \sqrt{3 x + 3}$

therefore
$\sqrt{x - 3} \sqrt{2 x - 1} = \sqrt{3 x + 3} s q u a r i n g o n b o t h s i d e s w e g e t (x - 3) (2 x - 1) = 3 x + 3 2 x^{2} = 10 x i m p l i e s x = 0, 5$

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