Subject: Best way to solve equations with logarithms?
From: Jaime E. Villate
Date: Thu, 9 Oct 2003 18:44:39 +0100
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