SOLUTION: 3^(2x)-30=3^x solve for 'x' with steps

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Question 872250: 3^(2x)-30=3^x
solve for 'x' with steps
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
3%5E%282x%29-30=3%5Ex
3%5E%282x%29-3%5Ex-30=0
Subsitute, u=3%5Ex, u%5E2=3%5E%282x%29
u%5E2-u-30=0
%28u-6%29%28u%2B5%29=0
Two u solutions.
u-6=0
u=6
and
u%2B5=0
u=-5
.
.
.
Since u=3%5Ex only the positive solution makes sense.
3%5Ex=6
x=log%283%2C%286%29%29
x=log%28%286%29%29%2Flog%28%283%29%29