Chemical Forums
Specialty Chemistry Forums => Other Sciences Question Forum => Topic started by: Riley_5000 on October 24, 2008, 05:24:50 AM
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I remember seeing a ln paradoxical proof a while ago. I can't remember it, so I came up with my own (I hope it's not the same!!)
say x =1
ln ((x^-2)/(x^2)) = 0
lnx^-2 - lnx^2 =0
lnx^-2 = lnx^2
-2lnx = 2lnx
-2 = 2
What do you think?
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(x-2/x2) = 1/x4. It does not equal 1.
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(x-2/x2) = 1/x4. It does not equal 1.
does when x = 1 though! ;)
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...
which is what op stipulated in his first statement...
no math in the morning for me...
carry on.
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As with all contradictory proofs, it involves division by zero. ln(x)=ln(1)=0.
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As with all contradictory proofs, it involves division by zero.
Not all, I have seen much more subtle one, using complex numbers :)
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Substitute "n" for "-2"
you get :
-n=n
It doesn't matter what x equals! Why do I do this to myself?
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ln ((x^-2)/(x^2)) = 0 is true only for x=1.
$$ log \left( \frac{(1/4)}{4} \right) = log(1/16) \neq 0 /$$
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I remember seeing a ln paradoxical proof a while ago. I can't remember it, so I came up with my own (I hope it's not the same!!)
say x =1
ln ((x^-2)/(x^2)) = 0
lnx^-2 - lnx^2 =0
lnx^-2 = lnx^2
-2lnx = 2lnx
-2 = 2
What do you think?
All of your expression are trues except the final step. Since lnx = 0 as x is equal to 1, you divide lnx for both sides i.e you divide 0 -> that's the mistake you've made.
Good luck :)