Just wondering, are there any useful tricks to make estimates of large powers or logarithms just by hand such as for $e^{10}$? Any such ways to get an error less than 1?
2026-04-03 04:51:08.1775191868
How can I make estimates on large powers and logarithms such as $e^{10}$?
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Many estimation methods exist.
For example, a popular and quick method to estimate the exponential function is using its power series:
$$e^x = 1 + x+ \frac{x^2}{2!}+\cdots$$ and this series can be used to obtain $\exp$ to a sufficient accuracy.
As for logarithms, using a series, such as the Taylor's series for $\operatorname {artanh}$, combined with pre-computed tables is an optimal way to compute logarithms numerically.