I've been working through a midterm practice problem and I ran into a little hitch with one. The answer it gives me is the last few steps of the equation but I am stuck between two of them.

The 2nd last step is a rearrange starting with-1/3ln|15-3I|=t+CI got to this step without an issue

Getting from the 2nd last step to the last is where it confuses me.I(t)=5-Cexp(-3t)

I multiplied the right side by -3 to give ln|15-3I|=3t+3C

then exponentiated to 15-3I=exp(3t)+exp(3C)

then -3I=exp(3t)+exp(3C)-15

and I=(-1/3)exp(3t)+exp(3C)-5

I'll admit my ln skills are getting a little rusty and maybe I've missed something obvious but I'm seriously stuck. Any help would be greatly appreciated. Thanks!

-Q