Is Log n Equal to Any of These Expressions for All Instances of n?

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Homework Statement



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The Attempt at a Solution



I believe log n does not equal any of these for all instances of n, but may for one specific instance...not entirely positive but I want to see what you guys think.
 
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Those formulas do not depend on n. It is a yes/no-decision for all 3 questions, and you need the definition of those symbols to solve it.
 
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All three are right.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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