Perfect LogarithmsDate: 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/ |
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