SOLUTION: If 3^(2x) + 9 = 10(3^x) solve for x. I know that x = 2 but only because of guess an check. I know I need to use a log somewhere and other basic algebra but I can't figure out wh

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Question 376226: If 3^(2x) + 9 = 10(3^x) solve for x.
I know that x = 2 but only because of guess an check. I know I need to use a log somewhere and other basic algebra but I can't figure out what all the steps are. I have looked through my book and some sites online and they didn't help.
Thanks!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let u=3%5Ex, then u%5E2=%283%5Ex%29%5E2=3%5E%282x%29,
u%5E2%2B9=10u
u%5E2-10u%2B9=0
%28u-1%29%28u-9%29=0
Two solutions:
u-1=0
u=1
3%5Ex=1
highlight%28x=0%29
.
.
.
u-9=0
u=9
3%5Ex=9
highlight%28x=2%29