Dva na x je enako x kvadrat

x=2 ?

in to sta tudi edini rešitvi... je rekel moj Derive

Yep, to so vse tri rešitve. Samo kako to, da postopka pa kr ni? Edini možni način reševanja je grafičen al kako?

Tudi simbolično z uporabo t.i. Lambert W funkcije se da to rešit.

http://www.apmaths.uwo.ca/~rcorless/frames/PAPERS/LambertW/

http://mathworld.wolfram.com/LambertW-Function.html

x^2 = 2^x
2*ln(x) = x*ln(2)
x/ln(x) = 2/ln(2)
obviously x = 2 but x = 4 also because 4/ln(4) = 4/(2*ln(2)=2/ln(2)

then,
x^2 = 2^x
x^2 = e^(x*ln(2))
x = +-e^(1/2*x*ln(2))

for x = -e^(1/2*x*ln(2))

x = -e^(a*x) implies that x = -W(a)/a
so we have x = -W(1/2*ln(2))/(1/2*ln(2)) = -2*W(1/2*ln(2))/ln(2).
Where W is the Lambert W function.

-2*W(1/2*ln(2))/ln(2) = -0.76666469596212309311120442251031484800667534666983205846088437

http://www.gamedev.net/community/forums/topic.asp?topic_id=212896

Kako bi pa rešu enačbe oblike a log x = b x ? Tut z Lambertovo W funkcijo?