Leading the way to the Future
 28 Oct 2009 03:23:09 pm by Flofloflo Hello, As the topic title suggests... I was busy with the harmonic series, so I was wondering: If there's a formula where the input of 2^x outputs 0.5 x. What's the formula? Now, my logic was: 2^x results in 0.5 x, x results in Ln(0.5x)/ln(2) = ln(0.5x)/ln(2) - 1. Apparently though, that is not the answer. I am totally unfamiliar with formula's where the input is not simply x... So could somebody help me out with this maybe? Btw, I already discovered that the answer is supposed to be 0.5 * (ln(x)/ln(2)), but I was wondering if there's a fast and logical way to find that? Actually, now that I think about it, maybe the way I found it out eventually was as logical as it gets: First I made a formula for a in 2^a = b, where b is your input, then I did 0.5*a... Okay, sorry I made this thread, I solved my own problem already... -.-
 28 Oct 2009 03:50:17 pm by GloryMXE7 you can simplify your formula to f(x)=.5ln(x-2) proof ln(x)/ln(2)=ln(x-2)
 GloryMXE7 wrote: you can simplify your formula to f(x)=.5ln(x-2) proof ln(x)/ln(2)=ln(x-2)
*facepalm*

What can I say? Thanks for testing that?
 28 Oct 2009 07:16:46 pm by FloppusMaximus GloryMXE7: check your math. Flofloflo: The function you're looking for is f(x) = log4 x (which is, of course, equivalent to ln x / ln 4, and can be written in many other ways besides.) In general, if you have some expression like f(2^x) = 0.5x, what you generally want to do is introduce another variable (say, u), define u = 2^x, and then try to replace the expression 0.5x with some expression in terms of u.