Prev: Possible simple bug in NMaximize
Next: WebMathematica problem
From: dimitris on 15 Nov 2006 07:24
Why Solve cannot deal with the following transcendental equation?

Solve[{2^x + 4^y == 9, x == y}, {x, y}]
\!\(Solve::"incnst" \(\(:\)\(\ \)\) "Inconsistent or redundant
transcendental equation. After reduction, the bad equation is
\!\(Log[2\
\^x]\/Log[2] - Log[2\^y]\/Log[2]\) == 0"\)
Solve::ifun: Inverse functions are being used by Solve, so some
solutions may \
not be found; use Reduce for complete solution information.
Solve::svars: Equations may not give solutions for all "solve"
variables.
{{x -> Log[2^y]/Log[2]}}

Reduce on the contrary works fine

Reduce[{2^x + 4^y == 9, x == y}, {x, y}]
C[1] ? Integers && (x == (2*I*Pi*C[1])/Log[2] + (I*Pi + Log[(1/2)*(1
+ Sqrt[37])])/Log[2] ||
x == (2*I*Pi*C[1])/Log[2] + Log[(1/2)*(-1 + Sqrt[37])]/Log[2]) && y
== x

and so does the following setting

Solve[2^x + 4^y == 9 /. y -> x, x]
Solve::ifun : Inverse functions are being used by Solve, so some
solutions \
may not be found; use Reduce for complete solution information.
{{x -> Log[(1/2)*(-1 + Sqrt[37])]/Log[2]}, {x -> (I*Pi + Log[(1/2)*(1 +
Sqrt[37])])/Log[2]}}

Dimitris

From: Bill Rowe on 16 Nov 2006 01:27
On 11/15/06 at 6:45 AM, dimmechan(a)yahoo.com (dimitris) wrote:

>Why Solve cannot deal with the following transcendental equation?
>
>Solve[{2^x + 4^y == 9, x == y}, {x, y}]

Because Solve simply isn't designed to address transcendental
equations efficiently if at all. Simply accept this as a
limitation of Solve. This particular equation is dealt with
quite efficiently using FindRoot, i.e.

In[3]:=
FindRoot[2^x + 4^x == 9, {x, 1.5}]

Out[3]=
{x->1.34561}

Given there are tools in Mathematica that can deal with such
equations, why worry that one particular tool doesn't work well?
--
To reply via email subtract one hundred and four

 | 
Pages: 1
Prev: Possible simple bug in NMaximize
Next: WebMathematica problem