SOLUTION: Solve the equation, show work,and give exact answers 10. [(e^x)-(e^-x)]/(2)= (-2)

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Question 369701: Solve the equation, show work,and give exact answers
10. [(e^x)-(e^-x)]/(2)= (-2)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
e%5Ex-e%5E%28-x%29=-4
e%5E%282x%29-1=-4e%5Ex
e%5E%282x%29%2B4e%5Ex-1=0
u%5E2%2B4u-1=0 where u=e%5Ex
u%5E2%2B4u%2B4-1-4=0
%28u%2B2%29%5E2=5
u%2B2=0+%2B-+sqrt%285%29
u=-2+%2B-+sqrt%285%29
e%5Ex=-2+%2B-+sqrt%285%29
highlight%28x=ln%28-2%2Bsqrt%285%29%29%29
The negative solution was removed since the natural log function requires a positive argument.