Taking the Logarithm of Zero

Date: 08/11/2004 at 05:31:35
From: Vijay
Subject: what is logarithm of zero?

Why is log(0) not defined?

Date: 08/11/2004 at 07:23:10
From: Doctor Ian
Subject: Re: what is logarithm of zero?

Hi Vijay,

Remember that any logarithmic statement can also be expressed as an
exponential statement and vice versa.  Thus,

if 

   a
  b  = c

then 

  log (c) = a
     b

                    3
For example, since 2  = 8, we can say log (8) = 3.
                                         2

So if 
  
  log (0) = a
     b

then 

   a
  b  = 0

but there's no way to raise a number to any power and end up with 
zero.  So log(0) is undefined. 

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/