Any 𝑥>0 can be written as a power series in 𝐥𝐧(x)pic.twitter.com/xlqM0JlC9G
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If you extend to the complex plane, I think this generalizes to all values of x? A quick check on Wolfram Alpha hasn’t disagreed. /shrugpic.twitter.com/0yivYlCvdb
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We usually exclude the logarithm for negative values because, for example, ln(-1) returns i*pi (e.g. a non-real). But if you sum out to infinity taking powers all those disappear. *waves hands* haha. I think..... lol.
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I think it's more the fact that e^z has the same series for complex z as it does for real z
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