ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: Chazef on March 16, 2013, 10:59:51 pm

Title: solve x=-ln(x)
Post by: Chazef on March 16, 2013, 10:59:51 pm

calculator says that x=0.567143.... and that more solutions may exist. I don't think this is in the course (at least not in the chapter I'm doing) but does anybody know the process for solving something like this?

Title: Re: solve x=-ln(x)
Post by: pi on March 16, 2013, 11:04:28 pm

Not unless you're familiar with uni concepts such as http://mathworld.wolfram.com/LambertW-Function.html :P

Title: Re: solve x=-ln(x)
Post by: brightsky on March 16, 2013, 11:07:37 pm

consider the function f(x) = x+ln(x). then compute the numerical approximation using newton's method [you make an initial guess, then find the x-intercept of the tangent line at that point and repeat a gazillion times until you are satisfied with the approximation]. very boring stuff.

you won't be asked to solve transcendental equations in methods.

Title: Re: solve x=-ln(x)
Post by: Chazef on March 16, 2013, 11:13:20 pm

reading stuff like that really makes me appreciate the awesomeness of math, even though I understood almost none of it
EDIT: was referring to that wolfram page