1. ## logarithms

Why is it that tha base of a logarithm can't be 1? I can't see anything wrong with this.
Thank you

2. ## 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.

3. ## Re: logarithms

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

$\displaystyle \log_ba=x \Leftrightarrow b^x=a$

$\displaystyle a>0$ and $\displaystyle b>0$

4. ## Re: 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.