How do you solve this exponential equation?

Question

$5^{2 x + 2} = \frac{1}{625}$ $5^(2x+2)=1/625$

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Answer 1 · 2016-11-13T23:23:33

Recall that $625 = 5^{3}$ $625 = 5^(3)$ .

$5^{2 x + 2} = 5^{- 3}$ $5^(2x + 2) = 5^-3$

Since we're in equal bases, we can eliminate and solve.

$2 x + 2 = - 3$ $2x + 2 = -3$

$2 x = - 5$ $2x = -5$

$x = - \frac{5}{2}$ $x = -5/2$

Hopefully this helps!