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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
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