Logarithmic Problem: Is There an Error?

  • Thread starter Nuclear on the Rocks
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In summary, the conversation discusses a problem involving the application of logarithm function to equations with positive numbers. The error is pointed out that the function is only defined for positive numbers and cannot be applied in this case. This leads to inconsistencies and contradictory results. The error is identified at the beginning of the equation and it is pointed out that dividing by zero leads to contradictions.
  • #1
Nuclear on the Rocks
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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.
 
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  • #2
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
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.
 

1. What is a logarithm?

A logarithm is a mathematical function that represents the power to which a fixed number, known as the base, must be raised to produce a given number.

2. How do logarithms relate to errors in scientific calculations?

In scientific calculations, logarithms are often used to represent very large or very small numbers in a more manageable form. This can help to reduce errors that may occur due to limited precision in calculations.

3. Can logarithms themselves contain errors?

No, logarithms are mathematical functions and are therefore exact. However, errors can occur when using logarithms in calculations due to human error or limitations in the technology used.

4. How can we identify errors in logarithmic calculations?

To identify errors in logarithmic calculations, it is important to check the inputs and ensure they are accurate, double check the calculations, and use different methods to verify the result.

5. Are there any common mistakes to watch out for when working with logarithms?

Yes, some common mistakes when working with logarithms include using the wrong base, forgetting to account for negative numbers, and forgetting to include the logarithm in the final answer.

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