write the expression as a single lograrithm, Express powers as factors.
ln((x/x-7))+ln((x+7/x))-ln(x^2-49)=______________

Question

write the expression as a single lograrithm, Express powers as factors.
ln((x/x-7))+ln((x+7/x))-ln(x^2-49)=______________

anonymous · Answer

$$\ln \frac{ a }{ b }=\ln a - \ln b$$$$\ln ab = \ln a + \ln b$$Factor x^2 -49 and you can do it easily.

anonymous · Answer

would this be it  $$(\ln(x)-\ln(x-7))+(\ln(x+7)-\ln(x))-(\ln(x+7)(x-7))$$  @Anonymous1921

anonymous · Answer

Yes. And ln[(x+7)(x-7)]=ln(x+7)+ln(x-7). So you can cancel out something.

anonymous · Answer

okay so it will look like wouldn't everything be cancel?

anonymous · Answer

@Anonymous1921

anonymous · Answer

I think -2ln(x-7) would be left. Check your calculation again. I might be wrong.

anonymous · Answer

so I got it to look like lnx-lnx-7+lnx+7-lnx-lnx-7+lnx+7

anonymous · Answer

then the lnx would be cancel and the lnx+7 would be cancel leaving -2lnx-7 ?

anonymous · Answer

ln(x)-ln(x-7)+ln(x+7)-ln(x)-ln(x+7)-ln(x-7). Oh, sorry. Everything would be cancelled out.

anonymous · Answer

really?? but the ln(x-7) doesnt get cancel out

anonymous · Answer

so wouldnt it be -2ln(x-7)

anonymous · Answer

Oh, yeah. -2ln(x-7).

anonymous · Answer

okay thanks you for the big help!

anonymous · Answer

You're welcome :)