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#