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Definite Integral as Limit of Sum

Solve the fol...

Question

Solve the following equation:
${log}_{5 - x} (x^{2} - 2 x + 65) = 2$

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Solution

$x^{2} - 2 x + 65 = (5 - x)^{2} x^{2} - 2 x + 65 = 25 + x^{2} - 10 x 8 x = - 40 x = - 5$

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