SOLUTION: 3^x + 9^x = 1/27

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Question 1080363: 3^x + 9^x = 1/27
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
9%5Ex=%283%5E2%29%5Ex=%283%5Ex%29%5E2
So then substituting u=3%5Ex,
u%2Bu%5E2=1%2F27
u%5E2%2Bu%2B1%2F4=1%2F27%2B1%2F4
%28u%2B1%2F2%29%5E2=31%2F108
u%2B1%2F2=0+%2B-+sqrt%2831%2F108%29
u=-1%2F2+%2B-+sqrt%2831%2F108%29
3%5Ex=-1%2F2+%2B-+sqrt%2831%2F108%29
Only positive right hand sides will give a real answer,
3%5Ex=-1%2F2%2Bsqrt%2831%2F108%29
x=log%283%2C%28sqrt%2893%29%2F18-1%2F2%29%29%29
highlight%28x=log%28%28sqrt%2893%29%2F18-1%2F2%29%29%2Flog%28%283%29%29%29%29