# How do you solve 4^(x-2) = 2^(3x+3)?

Jul 22, 2015

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#### Explanation:

${4}^{x - 2} = {2}^{3 x + 3}$

we know that, $4 = {2}^{2}$ , so:

${2}^{2 \cdot \left(x - 2\right)} = {2}^{3 x + 3}$

${2}^{2 x - 4} = {2}^{3 x + 3}$
Since the bases are equal we can now equate the respective powers:

$2 x - 4 = 3 x + 3$

$x = - 4 - 3$

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