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Please help explain what this means?

  1. May 28, 2014 #1
    I'm reading a book and there is a section about rules to do with logarithms but one of them I don't understand, it is very wordy and I just can't get what it means.

    It says "The logarithm of the power of a number is that power multiplied by the logarithm." I really don't understand what that means, can anyone who does break it down for me?
  2. jcsd
  3. May 28, 2014 #2
    [tex]\log (x^a) = a\log x[/tex]

    The logarithm "log" of the power "a" of a number "x" on the LHS, the power "a" multiplied by the logarithm [of that number] "log a" on the RHS.
  4. May 28, 2014 #3


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    If [itex]y= a^x[/itex] then [itex]x= log_a(y)[/itex]. That is often used as the definition of the logarithm. Exactly how was "[itex]log_a(x)[/itex]" defined in your class?
  5. May 28, 2014 #4
    How can x = the log of x? If we do 2^3 = 8 for example then log to the base 2 of 8 = 3, yes? I am still quite confused. I don't know why I can't understand this.
  6. May 28, 2014 #5


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    Who said ##x=\log(x)##?
    yes. It is correct.
    As HallsofIvy said before, if ##y=a^x## then ##\log_a(y)=x##.
    I understand it this way: To what power should x be raised to get y?
  7. May 28, 2014 #6
    I'm sorry, I misread HallsofIvy's post. I think I understand now.
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