Re: How to make the same two expressions
- To: mathgroup at smc.vnet.net
- Subject: [mg119586] Re: How to make the same two expressions
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Sat, 11 Jun 2011 03:58:52 -0400 (EDT)
- Reply-to: hanlonr at cox.net
expr1 = Rationalize[-1.0019 - 1. Log[0.00190438 - 0.0249519 b] + (0.000040093 a Log[0.152644/(0.152644 + 2 b)])/b, 0]; expr2 = Rationalize[-1.00004 - 1. Log[0.0000378969 - 0.0249519 b] + (0.000040093 a Log[0.0030376/(0.0030376 + 2 b)])/b, 0]; eqn = expr1 == expr2 // Simplify; Find instances that satisfy the equation soln = FindInstance[eqn, {a, b}, Reals, 4]; And @@ (eqn /. soln // Simplify) True soln // N {{a -> 250.968, b -> 0.000993046}, {a -> 253.051, b -> 0.00100671}, {a -> 83.7737, b -> -0.000955844}, {a -> 294.505, b -> 0.00122536}} Pick a value for a and solve for b FindRoot[eqn /. a -> 200, {b, 0.001}] {b -> 0.000568337} Reduce[eqn /. a -> 200, b, Reals] // N // ToRules {b -> 0.000568337} Solve[eqn /. a -> 200, b, Reals] // N {{b -> 0.000568337}} Or pick a value for b and solve for a FindRoot[eqn /. b -> 10^-3, {a, 200}] {a -> 252.023} Reduce[eqn /. b -> 10^-3, a, Reals] // N // ToRules {a -> 252.023} Solve[eqn /. b -> 10^-3, a, Reals] // N {{a -> 252.023}} Bob Hanlon ---- Mariano Pierantozzi <mariano.pierantozzi at gmail.com> wrote: ============= Hi everyone, i've this problem with Mathemtica: i've got 2 expression depending on a and b: expr1= -1.0019 - 1. Log[0.00190438 - 0.0249519 b] + (0.000040093 a Log[0.152644/(0.152644 + 2 b)])/b expr2=-1.00004 - 1. Log[0.0000378969 - 0.0249519 b] + (0.000040093 a Log[0.0030376/(0.0030376 + 2 b)])/b I want to make the same this two expressions. The problem is that if i try to solve this is one equation in two parameter: a and b. So i think to put inside some value of a and b so i make equal the two expression less than 10^-12 (for example) I've to do a list of value: b can vary beetwen -0.0015188 < b < 0.0015188 (the domain of logarithmic function) and a must vary for example -2000 to 2000. I can not find a waydo it. I try with list, and put the value inside, but i've some problem. if anyone can help I would be grateful... Thank you! Mariano Pierantozzi PhD student