Given the equation $5^{y + 4} = 25^{y + 3}$ , find the value of $y$ .

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Solution

The correct option is A $- 2$
$5^{y + 4} = 25^{y + 3}$
$\Rightarrow 5^{y + 4} = (5^{2})^{y + 3}$
$\Rightarrow 5^{y + 4} = 5^{2 y + 6}$
$∵$ base are same, so powers must be equal,
$\Rightarrow y + 4 = 2 y + 6$
$\Rightarrow y - 2 y = 6 - 4$
$\Rightarrow - y = 2$
$\Rightarrow y = - 2$

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