malcolmmcswain
  • malcolmmcswain
What is a Logarithm? (Tutorial)
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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malcolmmcswain
  • malcolmmcswain
What is a logarithm? A logarithm is, simply put, how to find how many times you have to multiply one number by itself to get another number. Here’s an example. How many times do you have to multiply 3 by itself to get 81? \[3*3*3*3=81\] Therefore, \[\log_{3}(81)=4 \] Let’s dissect this expression a bit. \[\log_{3}\] The little 3 after the log, called the base, is the number you have to multiply by itself. So, \[\log_{2}\] is how many times you have to multiply 2 by itself to get another number. We put the other number that we are trying to solve for in parentheses like this: \[\log_{2}(64)\] So, this just means, “How many times we have to multiply 2 by itself to get 64?”, and the answer to that is 6, because \[2*2*2*2*2*2=64\] So, \[\log_{2}(64)=6\]
malcolmmcswain
  • malcolmmcswain
Another way we can look at this is in exponential terms. One way to rephrase the expression \[\log_{9}(59,049)\] is “What power do we have to raise 9 to to get 59,049?” \[9^5=59,049\] So, \[\log_{9}(59,094)=5\] A more general way to quickly understand logarithms is to see the crossovers, illustrated below: |dw:1447171836116:dw| Logarithms can also be decimals: \[\log_{10}(50)=1.69897\] (approximately) because \[10^1.69897=50\] What about if we work backwards? How do we find the expression below? \[\log_{10}(0.001)\] Well, the only way to move backwards is to divide! \[1/10/10/10=0.001\] But, we didn’t multiply! Isn’t that breaking one of the rules of logarithms? Actually, \[10^-3=0.001\] So, \[\log_{10}(0.001)=-3\]
malcolmmcswain
  • malcolmmcswain
There are also other ways to write logarithms, for example, common logarithms are written without a base. \[\log(1000)\] When you encounter a common logarithm, never fear, this just means the base is 10. These are used quite a bit because a base of 10 is actually very common. \[\log(1000) = \log_{10}(1000) = 3\] Another way to write logarithms are natural logarithms, which always have a base of e. (e = Euler’s number = 2.71828…) These are written using ln instead of log. \[\ln(54.598...) = \log_{e}(54.598...) = 4\]

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More answers

AlexandervonHumboldt2
  • AlexandervonHumboldt2
nice work, great tutorial! First to answer, first to medal, first to say nice work, great tutorial! :)
AlexandervonHumboldt2
  • AlexandervonHumboldt2
sure
malcolmmcswain
  • malcolmmcswain
Thanks so much!
anonymous
  • anonymous
Cool! ur awesome at explaining it!
malcolmmcswain
  • malcolmmcswain
Once again, thank you!
IHelpYouLearn
  • IHelpYouLearn
This is an amazing tutorial! Great Job :)
malcolmmcswain
  • malcolmmcswain
Thanks :D
IHelpYouLearn
  • IHelpYouLearn
Absolutely no problem! Its really amazing and explained very well!
lochana
  • lochana
good work!
Nnesha
  • Nnesha
heya great work! o^_^o some tips you can use fraction like http://prntscr.com/91jfio and for exponent \[10^{1.69897}\] base^{exponent} you can add the formula how to convert log to an exponential form i guess that might help students to understand how u got \[10^{1.69897}=50\]
Nnesha
  • Nnesha
good job! keep it up!
malcolmmcswain
  • malcolmmcswain
Thank you all :D
DanJS
  • DanJS
exponents. good one
Owlcoffee
  • Owlcoffee
I think it's a good tutorial, but there is a huge lack of theorical background. It's not like a logarithm is an intuitive idea, it's a definition that was studied under some years before reaching what we currently know as "logarithm".
malcolmmcswain
  • malcolmmcswain
Hi all. I'm now realizing part of the tutorial is missing.
malcolmmcswain
  • malcolmmcswain
Posting it now.
malcolmmcswain
  • malcolmmcswain
Another way we can look at this is in exponential terms. One way to rephrase the expression \[\log_{9}(59,049)\] is “What power do we have to raise 9 to to get 59,049?” \[9^5=59,049\] So, \[\log_{9}(59,094)=5\] A more general way to quickly understand logarithms is to see the crossovers, illustrated below:
malcolmmcswain
  • malcolmmcswain
|dw:1447300069316:dw|
malcolmmcswain
  • malcolmmcswain
There we go.
DanJS
  • DanJS
I always just think log => exponent , nice little write up review
malcolmmcswain
  • malcolmmcswain
Yup.
malcolmmcswain
  • malcolmmcswain
@Owlcoffee This is more of an introductory tutorial... although I completely agree with you. Logarithms are just easier ways to write exponents.
malcolmmcswain
  • malcolmmcswain
Mathematicians are just lazy. :P
tkhunny
  • tkhunny
Logarithm is Exponent It may not be exactly the initial development of the concept, but that is where it landed.

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