SOLUTION: find x: 3^x - 3^-x = 4

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Question 1100499: find x:
3^x - 3^-x = 4
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
3%5Ex-1%2F3%5Ex=4
3%5E%282x%29-1=4%2A3%5E%282x%29
Use a substitution,
u=3%5Ex
u%5E2=3%5E%282x%29
So,
u%5E2-1=4u
u%5E2-4u-1=0
u%5E2-4u%2B4-1=4
%28u-2%29%5E2=5
u-2=0+%2B-+sqrt%285%29
u=2+%2B-+sqrt%285%29
3%5Ex=2+%2B-+sqrt%285%29
The negative sign would lead to a negative right hand side which is not a possible solution.
3%5Ex=2%2Bsqrt%285%29
x=log%283%2C%282%2Bsqrt%285%29%29%29
highlight%28x=log%28%282%2Bsqrt%285%29%29%29%2Flog%28%283%29%29%29