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Solve the fol...

Question

Solve the following equation:
$\frac{log (35 - x^{3})}{log (5 - x)} = 3$

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Solution

$\frac{log (35 - x^{3})}{log (5 - x)} = 3 => log (35 - x^{3}) = 3 log (5 - x) => log (35 - x^{3}) = log {(5 - x)}^{3} => 35 - x^{3} = {(5 - x)}^{3} => 35 - x^{3} = 125 - x^{3} + 15 x^{2} - 75 x => 15 x^{2} - 75 x + 90 = 0 => x^{2} - 5 x + 6 = 0 => x^{2} - 3 x - 2 x + 6 = 0 => (x - 3) (x - 2) = 0 ∴ x = 2, 3$

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