How did john Napier make log table I was just checking the log table and then suddenly It came to my mind that how were log tables made before calculators/computers how did john Napier calculate so precisely the values of $\log(2),\log(5),\log(7)$ etc . Is it even possible as I can't even estimate how much time it will take me to do this!! Did Napier use any sort of trick??

Humerous jokes aside about logs, what he did is if I recall correctly was that he worked with the base $1-10^{-7}$ and then computed it's various values at increasing values for numbers between $0$ and $1$. He then used the identity $$\log_a x = \frac{\log_b x}{\log_b a}$$ combined with other logarithmic identities to ease his computation, and I think he choose that value for base for simplicity reasons, which I cannot recall.