Logarithmic Problem: Is There an Error?

[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.

 

[Hurkyl]

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.

 

[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.