Perfect Logarithms

Date: 06/24/2002 at 06:41:15
From: Aga Khan
Subject: logarithm

For which values of a, b, and c is the equation

  log(abc) = log(a+b+c) 

true?  

Date: 06/25/2002 at 21:44:03
From: Doctor Jeremiah
Subject: Re: logarithm

Hi Aga,

There are an infinite number of answers because you have one equation
with three unknowns.  You can set two of the unknowns to any values
you want and solve the equation for the third, but since you can set
those two to an infinite number of different values there are an
infinite number of answers.

But perhaps you meant "for which INTEGER values..."

In that case consider this:

      log(abc) = log(a+b+c)

   10^log(abc) = 10^log(a+b+c)

           abc = a+b+c

The definition of a perfect number is that the product of the factors
is equal to the sum of the factors.  So that would mean that this
equation is true for a perfect number with three factors.

Its also true for a=0, b=0, and c=0...

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