Hi.. Anyone knows how to solve these kinds of expressions on a HP49:?
((40000*A+4000)/exp(A))=5000
Looks very simple, but just get the words:
"Not reducible to a rational expression"
Solving nonrational expressions on 49G?


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06162008, 07:12 AM
Hi.. Anyone knows how to solve these kinds of expressions on a HP49:? ((40000*A+4000)/exp(A))=5000
Looks very simple, but just get the words: ▼
06162008, 09:57 AM
I wouldn't even know how to solve this by hand but the numeric solver [RS][7] gives the following answer straight away A=2.863E2 You can also use ROOT which gives the same answer with a guess of 0. But a different answer with a guess of 2. So I don't know...
Edited: 16 June 2008, 10:01 a.m. ▼
06162008, 12:16 PM
Quote: Neither would I, but I have researched and have found the exact result is
where W(x) is [link:http://en.wikipedia.org/wiki/Lambert's_W_function]Lambert's W function[/link]. Please take a look at the general solution formula in example 1. I think this matches the numeric result you have found. Programs to compute the W function on the HP33S and some other HP calculators can be found
here. Regards, Gerson. ▼
06172008, 07:01 AM
Welcome back here, Gerson! (And congrats for your solution). JeanMichel.
06182008, 06:13 AM
Nice link. Spot on. Time to get back to do a bit of maths...
06162008, 01:00 PM
Quote:
I have just found out, thx to the numeric solver as you told me. Thanks
06172008, 01:30 AM
Equation to solve, using the HP49: ((40000*A+4000)/exp(A))=5000 which simplifies to 40*A  5*exp(A) + 4 = 0 whose derivative is 40  5*exp(A) Solving that for zero yields A = ln(8) ~= 2.079441542. This is the inflection point for the initial guess that determines which solution the HP15C gives, but not on the HP49G.
Quote: The "different" (but still valid) answer is 3.30455610804. My difficutly was figuring out how to copy 'n' paste the expression into the "NUM.SLV" form after symbolic solution "S.SLV" failed. I finally saved it to a variable and loaded that using "CHOOSE". (Sigh.) Once again, I would have had my answers so much faster with an ancient HP34C or HP15C, despite the vast difference in computational speed.  KS
Edited: 17 June 2008, 1:56 a.m. 