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Thanks
It is correct, but you can expand x^{2}-25 further. And note that |x|>5
Thanks
What ehild means in the last sentence is that you must have |x| > 5.It is correct, but you can expand x^{2}-25 further. And note that |x|>5
No, what he's saying is that you can factor x^{2} - 25.so instead of 25 it would be 5?
Yes, the expression can not be really expanded further for all x. Why was it marked incorrect then?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)##.
Just to be clear, that should be x^{2} - 25.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.I understand now. The x-25 could have been factored more. Thanks guys!