July 7th, 2010, 08:36 AM  #1 
Senior Member Joined: Jul 2009 Posts: 136 Thanks: 0  logarithms
A question in the text offers the following to simplify without using a calculator: log 27  log 3. I'm assuming (correctly?) that this would be [10 to the x power = 27]  [10 the x power = 3]. Anyway, the text answer is "3." But this doesn't make sense to me as obviously (once more!) I'm missing something. Any ideas? Thanks. 
July 7th, 2010, 09:02 AM  #2  
Member Joined: Nov 2009 Posts: 67 Thanks: 0  Re: logartihms Quote:
Use  
July 7th, 2010, 02:33 PM  #3 
Senior Member Joined: Jul 2009 Posts: 136 Thanks: 0  Re: logarithms
Thanks masters. But how would log9 = 3? That is the problem for me. If you can explain that, this would be great! Thanks.

July 8th, 2010, 10:57 AM  #4  
Member Joined: Nov 2009 Posts: 67 Thanks: 0  Re: logarithms Quote:
You text answer would seem to be incorrect if the log base is 10. If , then , and . Then the following woud be correct: only if the log base was  
July 8th, 2010, 03:49 PM  #5 
Senior Member Joined: Jul 2009 Posts: 136 Thanks: 0  Re: logarithms
OK, that was strange. Thanks for showing me that I'm not going crazy! And the one after it reads like this: (log 16  log 2 ) divided by log 2. The answer for this, according to the text, is also "3." But I am not getting that.... Help! 
July 8th, 2010, 03:59 PM  #6 
Senior Member Joined: Jul 2009 Posts: 136 Thanks: 0  Re: logarithms
By the way, what if we figure Log 27  Log 3? If the base, (b) was 3, then wouldn't we figure 3  1? But, again, I'm likely doing something wrong....

July 8th, 2010, 04:11 PM  #7  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond  Re: logarithms Quote:
 
July 9th, 2010, 08:30 AM  #8  
Senior Member Joined: Jul 2009 Posts: 136 Thanks: 0  Re: logarithms Quote:
 
July 9th, 2010, 08:33 AM  #9 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond  Re: logarithms
(log(16)  log(2))/log(2) = log(/log(2) = log(2^3)/log(2) = 3log(2)/log(2) = 3.

July 17th, 2010, 04:19 AM  #10  
Senior Member Joined: Jul 2009 Posts: 136 Thanks: 0  Re: logarithms
Thanks for the clear response but I have some questions as none of this is going by the rules given in the texts. 1. How did you go from log 16  log 2 to log 8? 2. If one says that it's a matter of log 16/log 2 then what's the point of restating it as a subtraction? 3. I would assume that log 16  log 2 = log 14. I know it's supposed to be the log of 16  the log of 2, but we do not know that the base number is but 10 here as nothing else is given as the base number. Quote:
 

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