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If $5^{x - 1} = 25^{x + 1}$ , then $x =$

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$- 3$

$3^{- 1}$

$(- 1) 3^{- 1}$

answer is A.

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Detailed Solution

$5^{x - 1} = 25^{x + 1}$

$5^{x - 1} = {(5^{2})}^{x + 1}$

$5^{x - 1} = 5^{2 x + 2}$ $\{∵ {(a^{m})}^{n} = a^{m n}\}$

$\Rightarrow$ $x - 1 = 2 x + 2$ $\{∵ a^{m} = a^{n} \Leftrightarrow m = n\}$

$- 1 - 2 = 2 x - x$

$- 3 = x$

$∴$ $x = - 3$

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