SOLUTION: Use the substitution u=3^x to solve the equation 3^x=4-3(3^-x).

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Question 716064: Use the substitution u=3^x to solve the equation 3^x=4-3(3^-x).
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
3%5Ex=4-3%2A3%5E%28-x%29
since 3%5E%28-x%29=1%2F3%5Ex
3%5Ex=4-3%2F3%5Ex
Substitute u=3%5Ex, u%3E0
u=4-3%2Fu
u%5E2-4u%2B3=0
%28u-3%29%28u-1%29=0
u-3=0 or u-1=0
u=3 or u=1
3%5Ex=3
3%5Ex=3%5E1
x=1
or
3%5Ex=3
3%5Ex=3%5E0
x=0
Answer: x=0, x=1