Logarithmic problem

  • #1
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.
 

Answers and Replies

  • #2
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
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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
367
1
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.
 

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