- #1
jumbogala
- 423
- 4
Homework Statement
Solve the equation for b.
db/dx = (e^2x)(e^2b) -- therefore:
db / (e^2b) = (e^2x)dx
Also note that b(0) = 8.
Homework Equations
The Attempt at a Solution
Following a list of steps my teacher gave me to solve these:
1) Integrate both sides.
-0.5 e^(-2b) = 0.5 e^(2x) + C
2) Isolate b.
e^(-2b) = -e^(2x) + C
-2b = ln(-e^(2x) + C)
And here we run into the problem - you can't take ln of a negative value!
If that e^(2x) was positive I would finish the problem like this:
2x + C = -2b
x is 0 and b is 8 so C has to be -16.
And my final answer would be b = -x + 8.
But, I didn't think you could do this if there's a negative inside ln?
Last edited: