MQ18 --- Exponential Equation
回答 (6)
2012-05-31 1:20 am
✔ 最佳答案
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
2012-05-30 12:35 am
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...
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...
2012-05-30 12:28 am
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.
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.
2012-05-29 4:02 am
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
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
2012-05-28 8:42 am
Maybe finding approximate solutions for the equation is more practical.
2012-05-28 7:41 am
Solving in R or in C will be very different. State exactly what you want.
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