Any ideas why this law of logs problem is marked incorrect?

  • #1
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ulTaMJU.png


Thanks
 

Answers and Replies

  • #2
ehild
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ulTaMJU.png


Thanks
It is correct, but you can expand x2-25 further. And note that |x|>5
 
  • #3
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so instead of 25 it would be 5?
 
  • #4
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It is correct, but you can expand x2-25 further. And note that |x|>5
What ehild means in the last sentence is that you must have |x| > 5.

so instead of 25 it would be 5?
No, what he's saying is that you can factor x2 - 25.
 
  • #5
ehild
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I also meant that the expression is not defined for |x| ≤ 5. You have to exclude it. And when expanding x2-25, log(x-5) is only defined if x>5,
 
  • #6
Fredrik
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The original expression is defined for all ##x## such that ##|x|>5##. (These values of ##x## make the thing under the square root positive). But ##\log(x-5)## is defined for all ##x## such that ##x>5##. So ##\log(x-5)## isn't defined for all ##x## such that the original expression makes sense. This seems like a good reason to not do the rewrite ##\log(x^2-25)=\log(x+5)+\log(x-5)##.
 
  • #7
ehild
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The original expression is defined for all ##x## such that ##|x|>5##. (These values of ##x## make the thing under the square root positive). But ##\log(x-5)## is defined for all ##x## such that ##x>5##. So ##\log(x-5)## isn't defined for all ##x## such that the original expression makes sense. This seems like a good reason to not do the rewrite ##\log(x^2-25)=\log(x+5)+\log(x-5)##.
Yes, the expression can not be really expanded further for all x. Why was it marked incorrect then?
 
  • #8
BruceW
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I'm guessing it is an online system which the answer is typed into, and automatically marked... So maybe it is because the 5 was placed right before the log, as in
5log, and maybe the computer did not recognize this as 5*log ?
 
  • #9
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I understand now. The x-25 could have been factored more. Thanks guys!
 
  • #10
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I understand now. The x-25 could have been factored more. Thanks guys!
Just to be clear, that should be x2 - 25.
 
  • #11
Fredrik
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I understand now. The x-25 could have been factored more. Thanks guys!
The ##x^2-25## can be factored, but we also said that it shouldn't be, because you don't want a final answer that makes sense for a smaller set of values of ##x## than the original expression. For example, the original expression makes sense when ##x=-7##, but an expression that contains ##\log(x-5)## doesn't. So we don't know why the answer you posted was marked incorrect. See BruceW's post for a possible reason.
 

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