# Logarithms, what are they?

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### #1 trotski

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# Logarithms, what are they?

Posted 16 September 2008 - 04:23 AM

I was doing Logarithms in school these days. I bet this is the most helpful forum ever on the WWW. I have always been helped. Now, I don't know why we use a calculator for finding the log of a number? Isn't there a formula? Of course, calculator uses a formula. Is this like the periodic table of elements, that each number has its own log? How long can this continue? Do the bases have anything to do with those in decimal, binary, hexadecimal, blah?

Wow, that sure is a fountain of questions, hope one is for answers too, thanks in advance.

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## Replies To: Logarithms, what are they?

### #2 Mikhail

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## Re: Logarithms, what are they?

Posted 16 September 2008 - 04:55 AM

You do realize this is the wrong forum?

• g+ + -o drink whiskey.cpp

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## Re: Logarithms, what are they?

Posted 16 September 2008 - 05:04 AM

That is a lot of questions I'm afraid I am not able to fully type out an answer at this time, but here are some links to get you started.

http://en.wikipedia.org/wiki/Logarithm

http://www.sosmath.c.../log1/log1.html

http://www.physics.u.../tutorials/LOG/

http://www.purplemat...odules/logs.htm

### #4 AmitTheInfinity

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## Re: Logarithms, what are they?

Posted 16 September 2008 - 05:07 AM

You had few right questions but in a very wrong place [Lounge? that can go to programming help -> Computer Science right? ]. So before you get flamed see here .

--EDIT--

This post has been edited by AmitTheInfinity: 16 September 2008 - 05:08 AM

### #5 PsychoCoder

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## Re: Logarithms, what are they?

Posted 16 September 2008 - 05:12 AM

Moved to Computer Science

### #6 trotski

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## Re: Logarithms, what are they?

Posted 16 September 2008 - 05:44 AM

++ thank you all for these suggestions. I am checking out all these. Also, I put this thread in Caffeine lounge and administrators moved it so I can't help. I have always posted all rubbish in Chit Chat Lounges of forums, may it be go4expert.com / ubuntuforums.org / linuxforums....

Sorry if it was incorrect.

### #7 trotski

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## Re: Logarithms, what are they?

Posted 17 September 2008 - 05:25 AM

... but after searching all trashcans on the net, I have even Googled and I don't get how to find the log of a number without a calculator. Could anybody help me out with a formula?

### #8 AmitTheInfinity

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## Re: Logarithms, what are they?

Posted 17 September 2008 - 05:39 AM

I am not sure whether you went through detailed contents of the links given in above posts. There are formulas to calculate logs, just find them carefully.

• g+ + -o drink whiskey.cpp

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## Re: Logarithms, what are they?

Posted 17 September 2008 - 06:31 AM

http://www.math.unc....logsnocalc.html

http://mathforum.org...view/68387.html

### #10 LowWaterMark

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## Re: Logarithms, what are they?

Posted 18 September 2008 - 11:18 PM

Logarithms are the exponent you have to raise any given base number to in order to get your number in question. It can be in base 10, commonly referred to as "log", and often the easiest to understand. Computer folks often do well getting the concept in binary, or base 2. Let's try both.

First, base 10, or "log".

100=10^2 therefor log100=2
1000=10^3 therefor log1000=3
1000000=10^6 therefor log1M=6

Now, binary or base 2 logarithms.

256=2^8 therefor log(base 2)256=8
512=2^9 therefor log(base 2)512=9
1024=2^10 therefor log(base 2)1024=10

Let me ask you a question. Log10=log(base 2)2. Given the above description, can you intuit what it is?

Finally, natural logarithms, or ln. People freak at natural logarithms. I've seen strong men cry over natural logarithms. I won't get into how they are derived, but I'll tell you what they do and why they are important. The natural log gives you the time needed to reach a certain level of continuous compounded growth. Period. That's it. This applies identically to decay, which is simply the inverse of growth.

There are two beautifully written pages of a site that describe natural logarithms (ln) better than I ever could. Read them patiently and in the order below:
An Intuitive Guide To Exponential Functions & E
Demystifying the Natural Logarithm (ln)

Hope this helps.

This post has been edited by LowWaterMark: 19 September 2008 - 01:05 AM

### #11 LowWaterMark

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## Re: Logarithms, what are they?

Posted 19 September 2008 - 05:47 AM

Sorry, one last thing.

When you are comfortable with natural logarithms (ln), and log(base 10), i.e. Log, and play around with getting the ln of a variable and Log of the same variable on either side of the equals sign (=). Move stuff around using the normal rules of exponents until you can see intuitively how Log and ln are related.

Be patient with yourself. It takes a bit to get the "aha" feeling with natural logarithms.

### #12 Programmist

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## Re: Logarithms, what are they?

Posted 20 September 2008 - 10:52 PM

In computer science log base 2 of X (denoted simple as lg X) is the most common log that you'll be dealing with. For instance, the height of a binary tree can be said to be in the set O(lg n) where n is the number of nodes in the tree. This also comes into play when determining the running time of some recursive algorithms (recurrences). For instance, the running time of the binary search algorithm can be expressed as T(n) = T(n/2) + O(1). It's easy to see that T(n) = O(lg n), as each recursion cuts the problem in half (no need for the master method).

### #13 trotski

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## Re: Logarithms, what are they?

Posted 21 September 2008 - 12:01 AM

Quote

Let me ask you a question. Log10=log(base 2)2. Given the above description, can you intuit what it is?

Yes. Log (base x) Y = 1 when x = Y. Naturally if we write in indical form, 2 Power 2 is 1 and 10 power 10 is one. Now my question was, that there are tables and massive books with logs of numbers. If we know how to that manually, we don't need those. When we do "log blah" in calculator, it gives a number that is log of blah. This is base 10 I know. We know these:

log base10 of blah = whatwedontknow. where we know the base and blah. Suppose we do log 7 in calculator. We get 0.84509804. The indical form is:

10 ^ 0.84509804 = 7. But how did the calculator get to find the power? There must be a formula?

What has the calculator done to blah?

### #14 RedSonja

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## Re: Logarithms, what are they?

Posted 22 September 2008 - 03:59 AM

Now I am so old and decrepit that I remember calculating the log of a number at school without a calculator. If my memory is not playing tricks, it was by plugging numbers into a convergent series.

In those days we used logs all the time for multiplying floats and for doing indices. You got the log out of a book; in the same book you could look up arctan and stuff. I think it is still there at the back of the cupboard. Do people still use logs, then? I thought they went out with the slide rule (which also works with logs, doesn't it?).

### #15 trotski

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## Re: Logarithms, what are they?

Posted 22 September 2008 - 04:13 AM

No, I don't have any book and everyone uses calculator. If this is slipping to technical side, then I better close this topic.