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Math Help - logarithms

  1. #1
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    logarithms

    Why is it that tha base of a logarithm can't be 1? I can't see anything wrong with this.
    Thank you
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  2. #2
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    e^(i*pi)'s Avatar
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    Re: logarithms

    The basic definition of a logarithm is \log_b(c) = a \Longleftrightarrow c = b^a

    If we say that b=1 then it follows that c = 1^a. Yet the laws of exponents say that if we raise 1 to any real number we get an answer of 1.
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  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: logarithms

    Quote Originally Posted by Nemesis View Post
    Why is it that tha base of a logarithm can't be 1? I can't see anything wrong with this.
    Thank you
    Hint:

    \log_ba=x \Leftrightarrow b^x=a

    a>0 and b>0
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  4. #4
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    Re: logarithms

    Another way of thinking about it is that " log_a(x)" is the inverse function to f(x)= a^x. But if a=1, f(x)= 1^x= 1, as e^(i*pi) pointed out. Because that function, unlike a^x for any other (positive) a, is not "one-to-one", it does not have an inverse.
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