       Re: Inverse function warnings

• To: mathgroup at smc.vnet.net
• Subject: [mg99237] Re: [mg99164] Inverse function warnings
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Thu, 30 Apr 2009 06:25:23 -0400 (EDT)

```eqn = 3^(2 x) - 12 (3^x) + 27 == 0;

Quiet[Solve[eqn, x]]

{{x -> 1}, {x -> 2}}

Off[Solve::ifun]

Solve[eqn, x]

{{x -> 1}, {x -> 2}}

{Reduce[eqn, x, Reals] // ToRules}

{{x -> 1}, {x -> 2}}

{Reduce[{eqn, Element[x, Reals]}, x] // ToRules}

{{x -> 1}, {x -> 2}}

Reduce[eqn, x]

Element[C, Integers] &&
(x == 1 + (2*I*Pi*C)/Log ||
x == 2 + (2*I*Pi*C)/Log)

This indicates that there are an infinite number of solutions. For any integer n

Simplify[eqn /. x -> 1 + 2 I*Pi*n/Log, Element[n, Integers]]

True

Simplify[eqn /. x -> 2 + 2 I*Pi*n/Log, Element[{n}, Integers]]

True

Bob Hanlon

---- davef <davidfrick2003 at yahoo.com> wrote:

=============
When I execute this in Mathematica 7:

Solve[3^(2 x) - 12 (3^x) + 27 == 0, x]

I get this:

Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. >>

{{x->1},{x->2}}

1 amd 2 are proper solutions but is it possible to avoid the warning?

If I use Reduce:

Reduce[3^(2 x) - 12 (3^x) + 27 == 0, x]

I get a set of 1 and 2 added to some imaginary number terms that I don't quite understand.

I guess my question is: why would the use of inverse functions be so unreliable a solution as to necessitate a warning?  And in the interest of clean output, can the warning be supressed other than by deleteing the cell?

Thanks

```

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