How do I solve x^x=50?

Answer 1

Numerically.

3.287262 < x < 3.287263

Answer 2

x^x = 50 = 50^1

log 50 = x
x
OR

log x^x = 1
50

This is what I get. But another stray method,
2^2 = 4
3^3 = 27
4^4 = 256

Hence, 3 < x < 4 could be the answer.

Answer 3

You have to use a numerical method.

For example, if you put the equation in the form x = ln(50)/ln(x)
and choose a suitable value for x on the right side you can solve for x on the left. use that value as the new x value on the right.

Repeat until you keep getting the same number.

There are other methods.

Answer 4

For all equations (and moreover systems of equations) that exist, there are two main methods that can applied to yield the solution,
(1) Analytic - This is applied when a real mathematic solution can be obtained, Im sure alot of mathematicians will be cursing me for classifying it in that nature, but basically we can get the exact solution. Theoretically one would assume that all equations are analytic but due to limited mathematical process' that exist we often have to approximate the solution.
(2) Numerical - (aka approximation) This methods apply iterative methods to approximate the solution to any degree of accuracy desired (generally). If an equation is deemed to not be analytic or the time taken to solve it is infesiable numerical methods are employed.
There are many applications of computational/numeric mathematics to solve for the solution of the non-linear equation provided. Examples of which are the bisection method, newtons method which can be found in any computational mathematical text.

Answer 5

If you have a grpahing calculator, then you can solve it graphically.
x^x = 50
Take the ln of each side
ln(x^x) = ln(50)
x*ln(x) = ln(50)

Graph each one separately.
y1 = x*ln(x) and y2 = ln(50)
Zoom in on the point of intersection, then use the intersect function to find the point of intersection.
x = 3.2872622

Answer 6

One other method is by using a graphing calculator:

y1=x^x
y2=50

And then find the point of intersection.

Answer 7

Difficult.

Answer 8

y1=x^x=x^2, y2=50

Answer 9

Try it numerically. Here is one method:

http://en.wikipedia.org/wiki/Newton's_method

Answer 10

x^x = 50

x = 3.28726