MQ18 --- Exponential Equation

圖片參考：http://i212.photobucket.com/albums/cc82/doraemonpaul/yahooknowledge/equation/transcendentalequation9.jpg

參考資料：
my wisdom of maths + formula from http://en.wikipedia.org/wiki/Lambert_W_function + http://en.wikipedia.org/wiki/Lagrange_inversion_theorem + http://en.wikipedia.org/wiki/Lagrange_reversion_theorem

I know.

But how to get exact value?

2012-05-29 17:41:49 補充：
Graphical method cant get exact value.

2012-05-31 22:01:01 補充：
Maybe this shouldn't be MQ18...

One is 2, another is around 0.346323

2012-05-29 17:03:05 補充：
Using bisection method, plot two graph, y = 1/(x-1) and y = log x / log 2,
one of the intersection point is 2 and the other lies between 0 and 1.

I'll try only.
xˣ= 2x
x^(x-1)=2
(x-1)log2(x)=1
because x ∈ C
so x-1=1, and log2(x)=1
x=2

sorry if it is wrong

Maybe finding approximate solutions for the equation is more practical.

Solving in R or in C will be very different. State exactly what you want.