# Logarithmic problem

1. May 9, 2007

### Nuclear on the Rocks

I an somewhat a layman, but i came across this problem. For any a & b, (b is not 0): ¤ a/b - a/b =0. [taking log to base 10 both sides] ¤ log(a/b - a/b) = log0. ¤ Log((a-a)/b) = log0. ¤Log(a-a) - logb = log0 ¤ log0 - logb = log0 ¤ -logb = log0-log0 ¤ -logb =0 ¤ -logb = log 1 [taking AL both sides] -b = 1. Can anyone point out the error here?There seems to be some inconsistancy.

2. May 9, 2007

### Hurkyl

Staff Emeritus
You should check to make sure you use actual carriage returns.

Anyways, your problem was right at the beginning -- the logarithm function is only defined for positive numbers. So, you cannot apply the logarithm function unless you can prove the two sides of the equation are positive.

3. May 9, 2007

### Moo Of Doom

First, log0 is not defined, so the entire logic falls apart there. This is about equivalent to dividing by zero, and we all know what contradictions that leads to...

Second, -logb = log1 implies 1/b = 1 not -b = 1.