# Proof via Logic

• December 15th 2012, 11:42 PM
DirectorRico
Proof via Logic
Could anyone help me with these questions?:

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

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Let a and b be non zero integers. Prove that a divides b and b divides a if and only if a = +/- b
• December 15th 2012, 11:49 PM
jakncoke
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
• December 16th 2012, 12:03 AM
DirectorRico
Re: Proof via Logic
Excellent! You're a great help.