And if you need some extra digits:

require(Rmpfr)
testfn<-function(x){2^x+3^x-13}
myint<-c(mpfr(-5,precBits=1000),mpfr(5,precBits=1000))
myroot<-unirootR(testfn, myint, tol=1e-30)
myroot

John Nash

On 13-10-11 06:00 AM, r-help-requ...@r-project.org wrote:
Message: 33
Date: Thu, 10 Oct 2013 21:03:00 +0200
From: Berend Hasselman<b...@xs4all.nl>
To: Ken Takagi<katak...@bu.edu>
Cc:r-h...@stat.math.ethz.ch
Subject: Re: [R] Looking for package to solve for exponent using
        newton's        method
Message-ID:<a12b1f57-a38f-470d-a6d7-479f94125...@xs4all.nl>
Content-Type: text/plain; charset="us-ascii"


On 10-10-2013, at 20:39, Ken Takagi<katak...@bu.edu>  wrote:

>Hi,
>I'm looking for an R function/package that will let me solve problems of the
>type:
>
>13 = 2^x + 3^x.
>
>The answer to this example is x = 2, but I'm looking for solutions when x
>isn't so easily determined. Looking around, it seems that there is no
>algebraic solution for x, unless I'm mistaken.  Does anyone know a good
>package to solve these types of problems? Are there built in functions to do
>this?
>
Univariate equations can be solved with uniroot, available in base R.

You can also use package nleqslv for this but that is intended for systems of 
nonlinear equations.
It does however solve your equation.
There is also BB which is especially intended for large sparse systems.

Berend


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