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

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Answer 1 · 2015-07-22T16:03:58

$color(blue)(x=-7$

$4^(x-2) = 2^(3x+3)$

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

$2^(2*(x-2)) = 2^(3x+3)$

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

$2x-4 = 3x+3$

$x=-4-3$

$color(blue)(x=-7$

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