text: # True or False?
  
  • Jun 29th 2011, 06:36 PM
  Googl
  True or False?
  Hi all,
  
  In this true or false?
  
  (5/2)ln(1-2x)-2ln(x) = -2ln(x)+(5/2)ln(2x-1)
  • Jun 29th 2011, 06:39 PM
  Krizalid
  Re: True or False?
  $a-b=-b+a,$ it's true, haha. :D
  • Jun 29th 2011, 06:45 PM
  Sudharaka
  Re: True or False?
  Quote:
  
  Originally Posted by Googl
  Hi all,
  
  In this true or false?
  
  (5/2)ln(1-2x)-2ln(x) = -2ln(x)+(5/2)ln(2x-1)
  
  Dear Googl,
  
  The equation is false. Substitute x=1.
  
  $\mbox{R.H.S}=0$
  
  $\mbox{L.H.S}=\frac{5i \pi}{2}$
  • Jun 29th 2011, 06:54 PM
  Krizalid
  Re: True or False?
  Oh, I misread it, I thought it was $1-2x$ on both sides.
  • Jun 29th 2011, 06:57 PM
  Googl
  Re: True or False?
  One of them is the correct result of an integration using partial fractions. For some reason (I don't know) some of the results are in this form -2ln(x)+(5/2)ln(2x-1) however the first one: (5/2)ln(1-2x)-2ln(x), note there is a pattern (2x-1) instead of (1-2x).
  
  This was for the integration of:
  
  (x+2)/(2x^2-x)
  
  Is there something I need to understand here?
  • Jun 29th 2011, 06:58 PM
  Krizalid
  Re: True or False?
  Remember to put absolute value to the logarithm.
explanation: The document contains a math question and a series of responses to that question. The initial post asks whether a given logarithmic equation is true or false. Subsequent responses provide evaluations of the equation, with one user confirming it is false by providing a counterexample.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # True or False?
  
  • Jun 29th 2011, 06:36 PM
  Googl
  True or False?
  Hi all,
  
  In this true or false?
  
  (5/2)ln(1-2x)-2ln(x) = -2ln(x)+(5/2)ln(2x-1)
  • Jun 29th 2011, 06:39 PM
  Krizalid
  Re: True or False?
  $a-b=-b+a,$ it's true, haha. :D
  • Jun 29th 2011, 06:45 PM
  Sudharaka
  Re: True or False?
  Quote:
  
  Originally Posted by Googl
  Hi all,
  
  In this true or false?
  
  (5/2)ln(1-2x)-2ln(x) = -2ln(x)+(5/2)ln(2x-1)
  
  Dear Googl,
  
  The equation is false. Substitute x=1.
  
  $\mbox{R.H.S}=0$
  
  $\mbox{L.H.S}=\frac{5i \pi}{2}$
  • Jun 29th 2011, 06:54 PM
  Krizalid
  Re: True or False?
  Oh, I misread it, I thought it was $1-2x$ on both sides.
  • Jun 29th 2011, 06:57 PM
  Googl
  Re: True or False?
  One of them is the correct result of an integration using partial fractions. For some reason (I don't know) some of the results are in this form -2ln(x)+(5/2)ln(2x-1) however the first one: (5/2)ln(1-2x)-2ln(x), note there is a pattern (2x-1) instead of (1-2x).
  
  This was for the integration of:
  
  (x+2)/(2x^2-x)
  
  Is there something I need to understand here?
  • Jun 29th 2011, 06:58 PM
  Krizalid
  Re: True or False?
  Remember to put absolute value to the logarithm.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and a series of responses to that question. The initial post asks whether a given logarithmic equation is true or false. Subsequent responses provide evaluations of the equation, with one user confirming it is false by providing a counterexample.
  
  Label: question-and-answer