Hey everyone! I'm currently in eighth grade. However, I decided over the weekend to learn about logarithms (I was bored). Surprisingly, logarithmic equations aren't as difficult as I expected them to be. Nevertheless, I have a few questions to ask.
1. When solving, if no base is specified should I assume that the natural logarithm or the common logarithm should be substituted? I read somewhere that mathematicians use Euler's number while engineers would use 10. What would students use? Does it depend on who your teacher is?
2. These are some specific logarithmic equation that I can't seem to get right no matter how many times I try to solve them. The funny thing is that I've already solved others like them. This is the question: Use logarithm laws to simplify the following.
i. log39xy2 - log327xy
ii. log39x4 - log3(3x)2
If someone could break them down step-by-step for me so that I would understand why I'm not getting them I would be extremely grateful.
3. Whenever I'm doing math I like to understand why something works, not just that it works. Therefore, can someone please explain this to me?
elog[3]a^(2)=a
I think that would read: E raised to the power of the logarithm of a with the base 2.
4. I promise this is the last thing! For now, anyway. How would I solve this?
The formula for the amount of energy E (in joules) released by an earthquake is
E = 1.74 x 1019 x 101.44M
i. The Newcastle earthquake in 1989 had a magnitude of 5 on the Richter scale.
How many joules were released?
ii. In an earthquake in San Francisco in the 1900's the amount of energy released
was double that of the Newcastle earthquake. What was its Richter magnitude?
I solved the first one correctly (E=2.757714126 joules), but when I change the second one to a logarithm . . . that's where I get stuck. I know I need to isolate the variable on one side of the equal sign, but what would the base be for the log? Wouldn't I have to somehow multiply 1.74 by 1019 by 101.44m without messing up m as my variable?
Thank you!
1. When solving, if no base is specified should I assume that the natural logarithm or the common logarithm should be substituted? I read somewhere that mathematicians use Euler's number while engineers would use 10. What would students use? Does it depend on who your teacher is?
2. These are some specific logarithmic equation that I can't seem to get right no matter how many times I try to solve them. The funny thing is that I've already solved others like them. This is the question: Use logarithm laws to simplify the following.
i. log39xy2 - log327xy
ii. log39x4 - log3(3x)2
If someone could break them down step-by-step for me so that I would understand why I'm not getting them I would be extremely grateful.
3. Whenever I'm doing math I like to understand why something works, not just that it works. Therefore, can someone please explain this to me?
elog[3]a^(2)=a
I think that would read: E raised to the power of the logarithm of a with the base 2.
4. I promise this is the last thing! For now, anyway. How would I solve this?
The formula for the amount of energy E (in joules) released by an earthquake is
E = 1.74 x 1019 x 101.44M
i. The Newcastle earthquake in 1989 had a magnitude of 5 on the Richter scale.
How many joules were released?
ii. In an earthquake in San Francisco in the 1900's the amount of energy released
was double that of the Newcastle earthquake. What was its Richter magnitude?
I solved the first one correctly (E=2.757714126 joules), but when I change the second one to a logarithm . . . that's where I get stuck. I know I need to isolate the variable on one side of the equal sign, but what would the base be for the log? Wouldn't I have to somehow multiply 1.74 by 1019 by 101.44m without messing up m as my variable?
Thank you!
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