malcolmmcswain
  • malcolmmcswain
What is a Logarithm? (A Tutorial)
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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, \[\log_{2}(64)=6\] 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, \[\log_{10}(0.001)=-3\] 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. \[\ln(54.598...) = \log_{e}(54.598...) = 4\]
malcolmmcswain
  • malcolmmcswain
Oops. This isn't turning out right...
AlexandervonHumboldt2
  • AlexandervonHumboldt2
First answer, First to say Great Tutorial, First to medal, first to everything GREAT TUTORIAL :) keep up nice work :).

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

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, \[\log_{2}(64)=6\] 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, \[\log_{10}(0.001)=-3\] 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. \[\ln(54.598...) = \log_{e}(54.598...) = 4\]
malcolmmcswain
  • malcolmmcswain
The full tutorial is too long.
AlexandervonHumboldt2
  • AlexandervonHumboldt2
you posted same thing?
malcolmmcswain
  • malcolmmcswain
I have to post it as 2 parts
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, \[\log_{2}(64)=6\] 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|
malcolmmcswain
  • malcolmmcswain
Thanks @AlexandervonHumboldt2 for the medal, but it looks like I'm going to have to repost this. This is my first tutorial, and I wrote it on a seperate post, so I could post it right away, but I made a bunch of mistakes.

Looking for something else?

Not the answer you are looking for? Search for more explanations.