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July 8th, 2010, 10:47 AM  #1 
Senior Member Joined: Jul 2009 Posts: 136 Thanks: 0  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? 
July 8th, 2010, 10:52 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond  Re: logarithms again!
If you use a base of then log 9 = 3.

July 8th, 2010, 11:01 AM  #3  
Member Joined: Nov 2009 Posts: 67 Thanks: 0  Re: logarithms again! Quote:
I followed up http://www.mymathforum.com/viewtopic.php?f=13&t=14865 in your original post.  
July 8th, 2010, 03:47 PM  #4  
Senior Member Joined: Jul 2009 Posts: 136 Thanks: 0  Re: logarithms again! Quote:
OK, but that's the problemthe text question is simply "Log 27  Log 3." I thought we assume a base of 10 if it is not noted.  
July 8th, 2010, 03:53 PM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond  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.

July 8th, 2010, 03:57 PM  #6  
Senior Member Joined: Jul 2009 Posts: 136 Thanks: 0  Re: logarithms again! Quote:
 
July 8th, 2010, 10:18 PM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,931 Thanks: 2205 
Maybe the intention was log(27)/log(3).

July 9th, 2010, 08:29 AM  #8  
Senior Member Joined: Jul 2009 Posts: 136 Thanks: 0  Re: Quote:
 
July 9th, 2010, 08:31 AM  #9 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond  Re: logarithms again!
log(27)/log(3) = log(3^3)/log(3) = 3log(3)/log(3) = 3.


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