Recent content by Ian Taylor

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    Undergrad Ln x as a logarithmic function

    Ah yes, but this means that big and yellow is not a 'good' definition of a banana. If we agree that it IS a good definition of a banana, then a mango would have to be called a banana. So if we agree on a definition of a logarithm, then any function which lives up to this definition must be a...
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    Solving a polynomial with complex coefficients

    Thanks SammyS. He had also written ##z^2## rather than ##z##. which contradicts his original definition.
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    Undergrad Ln x as a logarithmic function

    If we agree to define a logarithm as a function having certain properties, and we then find a function which has these defined properties then it must be a logarithm, by definition. You said it yourself: You can't have something which satisfies all the laws of logarithms which isn't a...
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    Undergrad Ln x as a logarithmic function

    Surely that's contradiction. If it satisfies the laws of logarithms then it is by definition a logarithm!
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    Solving a polynomial with complex coefficients

    ogg, I think you meant to write: Re##(z)=a^2-b^2## and Im##(z)=2ab##