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Math Help - Proof via Logic

  1. #1
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    Proof via Logic

    Could anyone help me with these questions?:

    Prove that there exists a unique real number x such that ln x = 2

    &

    Let a and b be non zero integers. Prove that a divides b and b divides a if and only if a = +/- b
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: Proof via Logic

    1)  ln x = 2 , is  e^{2} = x

    2)if a divides b then b = ak for some integer k, if b divides a, then a = bm for some integer m, so b = bmk, so mk = 1, since m and k are integers, either both m and k are -1, or both are positive 1. so either m = 1 so a = b or m = -1 and a = -b
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  3. #3
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    Re: Proof via Logic

    Excellent! You're a great help.
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