Best way to solve equations with logarithms?

HUh? it works for me  (the printout below may be scrambled because
it has tabs.)  Maxima 5.9.0


(C1)  2*log(3*x + 5) - 2*log(x) = y;
(D1)              2 LOG(3 x + 5) - 2 LOG(x) = y
(C2) %,logcontract;
                  2
                   9 x  + 30 x + 25
(D2)                LOG(----------------) = y
                       2
                      x
(C3) solve(%,x);
                   y/2         y/2
               5 %E       - 15         5 %E    + 15
(D3)             [x = - ------------, x = ------------]
                   y         y
                 %E  - 9           %E  - 9


If  you are objecting to the fact that there may be an extraneous root 
here, then I
think you will have to back-substitute and check any time you have a 
multi-valued
"function" in your problem, like log or square root.

RJF


Jaime E. Villate wrote:

>Hi,
>I've read the recent threads on log simplifications, but I still fail to
>find a general way to solve simple equations involving logarithms.
>
>For instance, solving, 2*log(3*x + 5) - 2*log(x) = y, for x.
>The best I've been able to do is:
>
>  (C2) eq: 2*log(3*x + 5) - 2*log(x) = y$
>
>  (C3) solve(ev(eq/2, ratsimp, logcontract), x);
>
>  (D3) [x = 5/(%E^(y/2)-3)]
>
>  (C4) build_info();
>  Maxima version: 5.9.0
>  Maxima build date: 19:17 9/9/2003
>  host type: i686-pc-linux-gnu
>  lisp-implementation-type: Kyoto Common Lisp
>  lisp-implementation-version: GCL-2-6.0999999999999996
>
>What I don't like about the method above is having to divide eq by 2 manually.
>If I don't do it, solve will not solve for x.
>
>Does anybody know of a better way to solve eq for x?
>
>Cheers,
>Jaime
>
>(with Cc to Herbert Desson, since this might be related to some thread
>he started recently)
>
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