ln(y) = -2x + c

Just did separation of variables. Solving for y (general solution). I cannot for the life of me figure out how to undo a natural log.

Question

ln(y) = -2x + c

Just did separation of variables. Solving for y (general solution). I cannot for the life of me figure out how to undo a natural log.

freckles · Answer

e^(ln(y))=y for y>0

freckles · Answer

$$y=e^{-2x+c}$$
you can make answer look prettier

anonymous · Answer

Woah. e^lny = y? Man, I need to relearn natural log stuff. That's not connecting for me at all

freckles · Answer

yes f(x)=ln(x) has inverse function g(x)=e^x
ans so f((g(x))=x and g(f((x))=x on their domains

freckles · Answer

$$y=ke^{-2x} \text{ since } e^c \text{ is a constant }$$

freckles · Answer

is what I meant about making the answer look prettier

anonymous · Answer

*Whistles*
Thanks

freckles · Answer

lol you whistled at a problem