Which of the following do not exist?

a) logarithms with fractional bases

b) logarithms of negative numbers

c) logarithms that equal zero

d) logarithms of irrational numbers

2 Answers

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  • 1 month ago

    Logarithms of negative numbers (exist in the complex number field but are not "real")

  • 1 month ago

    a) They exist, e.g. log[0.1](10) = -1

    b) They exist, although not real numbers, e.g. ln(-1) = i*pi = pi*sqrt(-1)

    c) This exists: log(1) = 0, in any base (except zero)

    d) They exist, e.g. log[10](sqrt(10)) = 0.5

    Answer: none of them do not exist, although (b) is not a real number

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