\(\displaystyle{{\log}_{{{5}}}{\left\lbrace-{3}\right\rbrace}}={\frac{{{\log{{\left({3}\right)}}}+\pi{i}}}{{{\log{{\left({5}\right)}}}}}}\)?

Alexis Alexander

Alexis Alexander

Answered question

2022-03-31

log5{3}=log(3)+πilog(5)?

Answer & Explanation

okusen8m1a

okusen8m1a

Beginner2022-04-01Added 8 answers

Complex logarithms are multivalued, since the exponential is periodic with period 2πi. Thus, properly speaking,
log5(3)=log(3)+πi+2nπilog(5)+2kπin,kZ
So, your calculator may be using different values of n and k from your n=k=0. In the vocabulary of complex analysis, we might say that your calculator is returning a value from a different branch than you expect.
Which calculator are you working with?

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