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July 8th, 2010, 10:47 AM   #1
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logarithms again!

The textbook answer for log 27 - log 3 is "3." But presuming that the base number is 10 how does this figure?

One responder here told me to see it as log 27/3 = log 9, but how does log 9 = 3? I think I'm missing something here....

If it were log(3) 9 then I would understand it better.... But the problem is just log 27 - log 3....

If anyone can explain this, then let me know....

Though I suppose it's possible the text is simply wrong?
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July 8th, 2010, 10:52 AM   #2
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Re: logarithms again!

If you use a base of then log 9 = 3.
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July 8th, 2010, 11:01 AM   #3
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Re: logarithms again!

Quote:
Originally Posted by empiricus
The textbook answer for log 27 - log 3 is "3." But presuming that the base number is 10 how does this figure?

One responder here told me to see it as log 27/3 = log 9, but how does log 9 = 3? I think I'm missing something here....

If it were log(3) 9 then I would understand it better.... But the problem is just log 27 - log 3....

If anyone can explain this, then let me know....

Though I suppose it's possible the text is simply wrong?
Hi empiricus,

I followed up http://www.mymathforum.com/viewtopic.php?f=13&t=14865 in your original post.
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July 8th, 2010, 03:47 PM   #4
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Re: logarithms again!

Quote:
Originally Posted by greg1313
If you use a base of then log 9 = 3.

OK, but that's the problem--the text question is simply "Log 27 - Log 3." I thought we assume a base of 10 if it is not noted.
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July 8th, 2010, 03:53 PM   #5
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Re: logarithms again!

Like you say, the text could be wrong, or perhaps you are expected to calculate the base given the result of log 9 = 3. I believe it is standard to assume a base of 10 if no base is given, though.
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July 8th, 2010, 03:57 PM   #6
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Re: logarithms again!

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Originally Posted by greg1313
Like you say, the text could be wrong, or perhaps you are expected to calculate the base given the result of log 9 = 3. I believe it is standard to assume a base of 10 if no base is given, though.
Well, that's just it. The answers are in the back and if it were something as Log(b) 9 = 3 then I would say sure, the b = 3, but all it presents is "Log 27 - Log 3" and an answer in the back of "3." Yikes!
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July 8th, 2010, 10:18 PM   #7
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Maybe the intention was log(27)/log(3).
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July 9th, 2010, 08:29 AM   #8
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Re:

Quote:
Originally Posted by skipjack
Maybe the intention was log(27)/log(3).
Oh, okay. Thanks. But then what would that be? Log (9)? The text answer is "3." I'm assuming at this point it's incorrect.
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July 9th, 2010, 08:31 AM   #9
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Re: logarithms again!

log(27)/log(3) = log(3^3)/log(3) = 3log(3)/log(3) = 3.
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