When you take a logarithm you’re asking “what power do I need to raise this base to, in order to get the given answer?”. For example, log2(8)=3, because 2³ =8.
You can take logs in any base, but the natural log uses the mathematical constant *e* as its base (~2.718).
As for ln(1)=0, this actually works in any base, as anything to the power of zero is equal to 1.
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