Steps on how to simplify log5/log125 to 1/3

  • Thread starter Gughanath
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  • #1
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could someone show me the steps on how to simplify log5/log125 to 1/3. I cant do it :grumpy:
 

Answers and Replies

  • #2
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Which base?
 
  • #3
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danne89 said:
Which base?
10, sorry for not mentioning that.
 
  • #4
dextercioby
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It doesn't matter the base,as long it is the same...:wink:

Daniel.
 
  • #5
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yes, so how could I simplify it?
 
  • #6
dextercioby
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[itex] 125=5^{3} [/itex] and use one definitory property of the logarithm...

Daniel.
 
  • #7
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hmmm....that comes to log5 to the power -2?
 
  • #8
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Why don't just: log5 125 = 3 and log5 5 = 1 and then just replace log 5 / log 125 = 1 / 3 ??
 
  • #9
dextercioby
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No,remember that in general:
[tex] \frac{\log a}{\log b}\neq \log\frac{a}{b} [/tex]

So pay attention to what u do.
Daniel.
 
  • #10
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log(125) = log(53) = 3log(5)
 
  • #11
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oh right. My bad. so log5/log125 = log5/log5^3 = log5/3log5, the log5's cancel, leaving 1/3. Thanx
 
  • #12
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And then cancel out the log(5)s, leaving 1/3?
 

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