I saw a final answer from a question:$\displaystyle \ln x=1$therefore$\displaystyle x=e$how they will become like this? What is $\displaystyle \ln$ and $\displaystyle e$? Is there any formula or rule for them?

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By definiton: ln(x) = y means e^y = x ln(x) = 1 then e^1 = x another way of looking at this is that ln(x) and e^x are inverses therefore e^(ln(x) = ln(e^x) = x so if ln(x) = 1 e^(ln(x)) = e^1 x = e