17 Replies  8470 Views  Last Post: 24 November 2009  03:29 PM
#1
Logarithms, what are they?
Posted 16 September 2008  04:23 AM
Wow, that sure is a fountain of questions, hope one is for answers too, thanks in advance.
Replies To: Logarithms, what are they?
#2
Re: Logarithms, what are they?
Posted 16 September 2008  04:55 AM
#3
Re: Logarithms, what are they?
Posted 16 September 2008  05:04 AM
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
Re: Logarithms, what are they?
Posted 16 September 2008  05:07 AM
EDIT
Amadeus gave more links, consider my post as void and go through his links.
This post has been edited by AmitTheInfinity: 16 September 2008  05:08 AM
#5
Re: Logarithms, what are they?
Posted 16 September 2008  05:12 AM
#6
Re: Logarithms, what are they?
Posted 16 September 2008  05:44 AM
Sorry if it was incorrect.
#7
Re: Logarithms, what are they?
Posted 17 September 2008  05:25 AM
#8
Re: Logarithms, what are they?
Posted 17 September 2008  05:39 AM
#9
Re: Logarithms, what are they?
Posted 17 September 2008  06:31 AM
#10
Re: Logarithms, what are they?
Posted 18 September 2008  11:18 PM
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
Re: Logarithms, what are they?
Posted 19 September 2008  05:47 AM
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
Re: Logarithms, what are they?
Posted 20 September 2008  10:52 PM
#13
Re: Logarithms, what are they?
Posted 21 September 2008  12:01 AM
Quote
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
Re: Logarithms, what are they?
Posted 22 September 2008  03:59 AM
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
Re: Logarithms, what are they?
Posted 22 September 2008  04:13 AM
