[R] solve the equation in R

[Petr Savicky]

On Thu, May 17, 2012 at 01:53:39PM -0500, Pei-Ling Lin wrote:
> Hi all,
> 
> I need to solve this following equation which the unknown value (here is "a") is on the exponent place, could anybody please help me to figure it out? I tried to use lm.sol() or solve() function but it doesn't work...... 
> 
> Thanks for help,
> Peiling 
> 
> 
>   (x,   y) = (2.21, 1.01)
> 
>   y = 1 + x - ( 1 + (x)^a)^(1/a)

Hi.

First, plot the function

  f <- function(a) { 1 + x - ( 1 + (x)^a)^(1/a) - y }
  x <- 2.21
  y <- 1.01
  a <- seq(0.1, 20, length=1000)
  plot(a, f(a), ylim=c(-0.2, 0.2), type="l")
  abline(h=0)

This suggests, that there is no root. This may also be obtained
analytically.

Hope this helps.

Petr Savicky.