slove this equation in R (x)^(x^8)=8?

Answer 1

This is what I did:

1. Define a function that is equal to the function subtracted by 8 and then squared. Subtracting by 8 makes the value that you are look for the zero of the function, so squaring would make it the minimum.

> f <- function(x)
+ {
+ (x^(x^8)-8)^2
+ }

This would make the number you are looking for the minimum of this expression.

2. Use the function nlm to minimize the function.

> b <- nlm(f, 1)$estimate

f is the function I defined, and I told the function to start looking at a value of 1, since it seems that the minimum will be close to 1. Take a look at ?nlm (the help on nlm) to see what else can be defined.

Note: I got some warning messages because this function becomes infinite if the eyes of R very quickly. That doesn't effect the optimization.

3. b is then the value that solves your equation.

> b
[1] 1.296839
> b^(b^8)
[1] 7.999966

If this is not close enough for you, then work with the nlm function. You will have to adjust the gradtol value (its default is 1e-6).

There is probably another way of doing this, but since I'm familiar with nlm, this is how I would do it.

edit: Sorry, this is answer for the statistical software R. I got it confused with R meaning the real line. I don't believe that you can solve the equation analytically; it probably needs to be done using optimization.

Answer 2

22=-7/10+r? Isolate the 'r' by potential of bringing each little thing over to a minimum of one part of the equals sign different than for the 'r' and keep in mind that when something is taken over an equals sign the sign ameliorations: 22+ 7/10 = r r= 22 7/10 or 22.7

Answer 3

x = 1.297 (approximately)
but hey thats not "slove" thats "solve"

Answer 4

x lies between 1 and 2.

Answer 5

x is between 1.296 and 1.298

Answer 6

1.2968395546510096