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Logarithmic Differentiation

Solve the fol...

Question

Solve the following equation:
$log (3 x^{2} + 7) - log (3 x - 2) = 1$

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Solution

$l o g ({3 x}^{2} + 7) - l o g (3 x - 2) = 1 \frac{{3 x}^{2} + 7}{3 x - 2} = 10 {3 x}^{2} + 7 = 30 x - 20 {3 x}^{2} - 30 x + 27 = 0 x^{2} - 10 x + 9 = 0$

$∴ x = 1, 9$

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