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This is an archived, readonly copy of the UnitedTI subforum , including posts and topic from May 2003 to April 2012. If you would like to discuss any of the topics in this forum, you can visit Cemetech's Technology & Calculator Open Topic subforum. Some of these topics may also be directlylinked to active Cemetech topics. If you are a Cemetech member with a linked UnitedTI account, you can link UnitedTI topics here with your current Cemetech topics.
Math and Science => Technology & Calculator Open Topic
Author 
Message 

Flofloflo
Member
Joined: 07 Nov 2007 Posts: 120

Posted: 28 Oct 2009 03:23:09 pm Post subject: 


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... .
Last edited by Guest on 28 Oct 2009 03:35:26 pm; edited 1 time in total 

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GloryMXE7 Puzzleman 3000
Active Member
Joined: 02 Nov 2008 Posts: 604

Posted: 28 Oct 2009 03:50:17 pm Post subject: 


you can simplify your formula to f(x)=.5ln(x2)
proof
ln(x)/ln(2)=ln(x2)
Last edited by Guest on 28 Oct 2009 03:52:55 pm; edited 1 time in total 

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Weregoose Authentic INTJ
Super Elite (Last Title)
Joined: 25 Nov 2004 Posts: 3976

Posted: 28 Oct 2009 03:58:06 pm Post subject: 


GloryMXE7 wrote:  you can simplify your formula to f(x)=.5ln(x2)
proof
ln(x)/ln(2)=ln(x2)  *facepalm*
What can I say? Thanks for testing that?
Last edited by Guest on 28 Oct 2009 03:58:23 pm; edited 1 time in total 

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FloppusMaximus
Advanced Member
Joined: 22 Aug 2008 Posts: 472

Posted: 28 Oct 2009 07:16:46 pm Post subject: 


GloryMXE7: check your math.
Flofloflo: The function you're looking for is f(x) = log_{4} 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. 

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