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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- Jul 6th 2011, 03:27 PMNemesislogarithms
Why is it that tha base of a logarithm can't be 1? I can't see anything wrong with this.

Thank you - Jul 6th 2011, 03:33 PMe^(i*pi)Re: logarithms
The basic definition of a logarithm is $\displaystyle \log_b(c) = a \Longleftrightarrow c = b^a$

If we say that $\displaystyle b=1$ then it follows that $\displaystyle c = 1^a$. Yet the laws of exponents say that if we raise 1 to any real number we get an answer of 1. - Jul 6th 2011, 03:42 PMAlso sprach ZarathustraRe: logarithms
- Jul 7th 2011, 12:17 PMHallsofIvyRe: logarithms
Another way of thinking about it is that "$\displaystyle log_a(x)$" is the inverse function to $\displaystyle f(x)= a^x$. But if a=1, $\displaystyle f(x)= 1^x= 1$, as e^(i*pi) pointed out. Because that function, unlike $\displaystyle a^x$ for any other (positive) a, is not "one-to-one", it does not have an inverse.