Maxima's knowledge of the properties of log is not localized, but spread
out over various subsystems, including numerical evaluation, solve, taylor
series, integration, differentiation, limits, simplification, logcontract,
etc.
Once you get into calculus operations, it becomes clear why log base *e* is
called "natural" -- for example, diff(log10(x),x) => 1/(x*log(10)), but
diff(log(x),x)=>1/x.
A simple approach is to convert log10 to log, perform the calculation, then
convert from log back to log10, like this:
log10_to_log(ex) := subst(lambda([x],log(x)/log(10)),'log10,ex)$
log_to_log10(ex) := subst(lambda([x],log10(x)*log(10)),'log,ex)$
For example,
eq: log10(x)+3=log10(x+1);
eq1: log10_to_log(eq);
load(to_poly_solve)$ <<< good for equations with multiple logs
%solve(eq1,x);
=> %union([x = 1/999])
In this case, there aren't even any logs in the result, so no conversion
back to log10 is necessary.
In general, the log_to_log10 part should be a bit more elaborate, so that
log10(100)=>2 and so on.
-s
On Tue, May 14, 2013 at 5:46 PM, Bill Eaton <wpeaton4 at gmail.com> wrote:
> **
> I have an interest in being able to do useful symbolic and numeric
> calculations with logarithms in base 10. I know there is a contrib module
> called log10. It works fine for doing numeric calculations, but doesn't
> behave how I'd like for generic symbolic manipulation.
>
> For example the natural log can solve for x:
> (%i1) solve(y=log(x),x);
> (%o1) [x=%e^y]
>
> But log10 gives this:
> (%i2) solve(y=log10(x),x);
> (%o2) [log10(x)=y] /* I'd prefer to get x=10^y */
>
> There are many of other examples of symbolic manipulation of log10 where
> log shows up in the answer. I'd really like to leave log out of it
> altogether.
>
> It would be really handy if I could teach Maxima the various properties of
> logarithms and inverse logarithms. My interest is base 10, but it seems
> that it would be fairly generic for other integer bases.
>
> I don't even know where to start, but suggestions are welcome.
>
> Thanks in advance,
>
>
> Bill Eaton
>
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>