# logarithms

• Jul 6th 2011, 03:27 PM
Nemesis
logarithms
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 PM
e^(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 PM
Also sprach Zarathustra
Re: logarithms
Quote:

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\$
• Jul 7th 2011, 12:17 PM
HallsofIvy
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.