Gday Dampf
If that method isnt accurate enough for you, and you have floating point routines, you may want to look at
http://www.dattalo.com/technical/theory/logs.html
Section 5 gives the taylor series method of calculating ln(x), and you can expand this as far as reqd to get the accuracy you require. Not sure if the pic will handle the calcs though )
If it can, then you just use the same method as before to reduce back to log10.
I havent used this method with a PIC, but it may help with what you are trying to do.
Andrew