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Laws of Exponents for Real Numbers

Solve: 252 x...

Question

Solve:
$25^{2 x - 3} = 5^{2 x + 3}$

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Solution

$25^{2 x - 3} = 5^{2 x + 3}$
$5^{2 (2 x - 3)} = 5^{2 x + 3}$
$5^{4 x - 6} = 5^{2 x + 3}$
$⟹ 4 x - 6 = 2 x + 3$
$⟹ 2 x = 9$
$⟹ x = \frac{9}{2}$

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