SOLUTION: (9^x)^2=81*9^x+3

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Question 1080342: (9^x)^2=81*9^x+3
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let u=9%5Ex, then
u%5E2=81u%2B3
u%5E2-81u=3
u%5E2-81u%2B%2881%2F2%29%5E2=3%2B%2881%2F2%29%5E2
%28u-81%2F2%29%5E2=12%2F4%2B6561%2F4
%28u-81%2F2%29%5E2=6573%2F4
u-81%2F2=0+%2B-+sqrt%286573%29%2F2
u=81%2F2+%2B-+sqrt%286573%29%2F2
9%5Ex=81%2F2+%2B-+sqrt%286573%29%2F2
Only positive solutions make sense here,
9%5Ex=81%2F2+%2B+sqrt%286573%29%2F2
x=log%289%2C%2881%2F2+%2B+sqrt%286573%29%2F2%29%29
highlight%28x=log%28%2881%2F2+%2B+sqrt%286573%29%2F2%29%29%2Flog%28%289%29%29%29