Best way to solve equations with logarithms?



On Thu, Oct 09, 2003 at 09:03:31AM -0700, Richard Fateman wrote:
> 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

Your right; that works for me to. What happened was that I simplified
the example to send it to the list. The actual case where it fails is:

(D5) 35*LOG(3*x+5)-35*LOG(x) = y
(C6) %, logocontract;

(D6) 35*LOG(3*x+5)-35*LOG(x) = y
(C7) %, logcontract;

(D7) LOG((50031545098999707*x^35+2918506797441649575*x^34
                                +82691025927513404625*x^33
                                +1516002142004412418125*x^32
                                +20213361893392165575000*x^31
                                +208871406231719044275000*x^30
                                +1740595051930992035625000*x^29
                                +12018394406190183103125000*x^28
                                +70107300702776068101562500*x^27
                                +350536503513880340507812500*x^26
                                +1518991515226814808867187500*x^25
                                +5753755739495510639648437500*x^24
                                +19179185798318368798828125000*x^23
                                +56554009405297754150390625000*x^22
                                +148117643680541737060546875000*x^21
                                +345607835254597386474609375000*x^20
                                +720016323447077888488769531250*x^19
                                +1341206877009262733459472656250*x^18
                                +2235344795015437889099121093750*x^17
                                +3333408904847582817077636718750*x^16
                                +4444545206463443756103515625000*x^15
                                +5291125245789813995361328125000*x^14
                                +5611799503110408782958984375000*x^13
                                +5286477792785167694091796875000*x^12
                                +4405398160654306411743164062500*x^11
                                +3230625317813158035278320312500*x^10
                                +2070913665264844894409179687500*x^9
                                +1150507591813802719116210937500*x^8
                                +547860758006572723388671875000*x^7
                                +220403753221035003662109375000*x^6
                                +73467917740345001220703125000*x^5
                                +19749440252780914306640625000*x^4
                                +4114466719329357147216796875*x^3
                                +623404048383235931396484375*x^2
                                +61118043959140777587890625*x
                                +2910383045673370361328125)
          /x^35)
       = y
(C8) %, solve;

(D8) LOG((50031545098999707*x^35+2918506797441649575*x^34
                                +82691025927513404625*x^33
                                +1516002142004412418125*x^32
                                +20213361893392165575000*x^31
                                +208871406231719044275000*x^30
                                +1740595051930992035625000*x^29
                                +12018394406190183103125000*x^28
                                +70107300702776068101562500*x^27
                                +350536503513880340507812500*x^26
                                +1518991515226814808867187500*x^25
                                +5753755739495510639648437500*x^24
                                +19179185798318368798828125000*x^23
                                +56554009405297754150390625000*x^22
                                +148117643680541737060546875000*x^21
                                +345607835254597386474609375000*x^20
                                +720016323447077888488769531250*x^19
                                +1341206877009262733459472656250*x^18
                                +2235344795015437889099121093750*x^17
                                +3333408904847582817077636718750*x^16
                                +4444545206463443756103515625000*x^15
                                +5291125245789813995361328125000*x^14
                                +5611799503110408782958984375000*x^13
                                +5286477792785167694091796875000*x^12
                                +4405398160654306411743164062500*x^11
                                +3230625317813158035278320312500*x^10
                                +2070913665264844894409179687500*x^9
                                +1150507591813802719116210937500*x^8
                                +547860758006572723388671875000*x^7
                                +220403753221035003662109375000*x^6
                                +73467917740345001220703125000*x^5
                                +19749440252780914306640625000*x^4
                                +4114466719329357147216796875*x^3
                                +623404048383235931396484375*x^2
                                +61118043959140777587890625*x
                                +2910383045673370361328125)
          /x^35)
       = y
(C9) 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