Re: interesting equation

On 15 août, 21:47, Robert Israel
<isr...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
Tolstoy <kellrobin...@xxxxxxxxxxxx> writes:
Doing analysis on a circuit I ended up with

2^(1+r) = (2r-1)/(r-2)

where r is the ratio between the values of two resistors.

I fiddled with the calculator and got 2.362...

How does one determine whether such an equation has a closed-form
solution or one has to resort to iterative calculations?
Not a pressing issue, just thought it was interesting.

Maple doesn't come up with a closed-form solution, so I guess there
isn't one. Equations where the variable occurs both in an exponent
and by itself usually don't have closed-form solutions, unless they
can be related to the Lambert W function (which apparently this one
can't).
--
Robert Israel isr...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada

Bonjour,

The equation may be written :
2^(2*r-1)/(2*r-1) = 2^(r-2)/(r-2)
An obvious solution is 2*r-1 = r- 2 ; r = -1 .
....
Alain

.

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