Is There an Algebraic Solution for 36=X^X?

[Freespader]

I came up with an idea for an equation, which follows: 36=X^X. I tried solving it, but I couldn't. I found the graphically (3.15, if I recall correctly), but I want to know if there's a way to solve it algebraically.

 

[tiny-tim]

… I want to know if there's a way to solve it algebraically.

nope!

 

[Char. Limit]

Actually, you can, but you need to use the Lambert-W Function.

 

[RamaWolf]

Let f(x):=x$^{x}$ - 36, (f(x) is continuous, f(3.1) < 0, f(3.2) > 0) we can apply

the 'half intervall' function I implemented in my ARIBAS_W workbench, to find the zero of f(x)

in the intervall (3.1,3.2) as: 3.13564239388907368

 

[blue_raver22]

There is not a simple algebraic solution for this equation. It is known as a transcendental equation, meaning it cannot be solved using basic algebraic methods. However, it can be approximated using numerical methods such as the Newton-Raphson method or the bisection method. These methods involve using a computer or calculator to find a numerical solution. Alternatively, you can also use a graphing calculator to find the intersection of the two graphs of y=36 and y=x^x. I hope this helps!