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Exponents with Like Bases

Solve the fol...

Question

Solve the following equation:
${(\frac{5}{3})}^{x + 1} \cdot {(\frac{9}{25})}^{x^{2} + 2 x - 11} = {(\frac{5}{3})}^{9}$

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Solution

$(\frac{5}{3})^{x + 1} \cdot (\frac{9}{25})^{x^{2} + 2 x - 11} = (\frac{5}{3})^{9}$
$(\frac{5}{3})^{x + 1 - 2 x^{2} - 4 x + 22} = (\frac{5}{3})^{9}$
$- 2 x^{2} - 3 x + 23 = 9$
$2 x^{2} + 3 x - 14 = 0$
$2 x^{2} + 4 x - 7 x - 14 = 0 ⟹ x = - 2, \frac{7}{2}$

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