You can put this solution on YOUR website! 5e^x = 9-e^(-x)
Multiply both sides by e^x:
5e^(2x) = 9e^x-1
1-9e^x+5e^(2x) = 0
1-9e^x+5e^(2x) = 1-9e^x+5(e^x)^2 = 5y^2-9y+1 = 0
So now I have:
5y^2-9y+1 = 0
y^2-(9y)/5+1/5 = 0
y^2-(9y)/5 = -1/5
Add 81/100 to both sides:
y^2-(9y)/5+81/100 = 61/100
(y-9/10)^2 = 61/100
y-9/10 = sqrt(61)/10 or y-9/10 = -sqrt(61)/10
Add 9/10 to both sides:
y = 9/10+sqrt(61)/10 or y-9/10 = -sqrt(61)/10
Substitute back for y = e^x:
e^x = 9/10+sqrt(61)/10 or y-9/10 = -sqrt(61)/10
x = log(9/10+sqrt(61)/10)+2ipin_1 for n_1 element Z
or y-9/10 = -sqrt(61)/10
Add 9/10 to both sides:
x = log(9/10+sqrt(61)/10)+2ipin_1 for n_1 element Z
or y = 9/10-sqrt(61)/10
Substitute back for y = e^x:
x = log(9/10+sqrt(61)/10)+2ipin_1 for n_1 element Z
or e^x = 9/10-sqrt(61)/10
Take the natural logarithm of both sides to get your answer:
x = log(9/10+sqrt(61)/10)+2ipin_1 for n_1 element Z
or x = log(9/10-sqrt(61)/10)+2ipin_2 for n_2 element Z
