Thread: logarithms

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

The basic definition of a logarithm is

If we say that then it follows that . Yet the laws of exponents say that if we raise 1 to any real number we get an answer of 1.

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:



and

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