1.
y-9=e2x Add 9 to both sides y = e^(2x) + 9
3=y-7ex Subtract 7e^x to both sides y = 3 + 7e^x
Set the y's equal
e^(2x) + 9 = 3 + 7e^x rearrange as
e^(2x) - 7e^x + 6 = 0 factor
(e^x - 6)(e^x - 1) = 0 set each factor to 0 and solve
e^x - 6 = 0
e^x = 6 take the Ln of both sides
Ln e^x = Ln 6 and we can write
x * Ln e = Ln 6
x = Ln 6
Using a similar proceedure
x = Ln 1 = 0
So.....the two solutions are x = Ln 6 and x = 0
