17 окт. 2014 г. · There is no polynomial or rational approximation to ln(x) that is accurate for all large x.

7 янв. 2021 г. · I saw on https://math.stackexchange.com/a/2382470/432488 the following approximation: ln(x)≈ax1/a−a, which is good for large value of a. Where ...

4 мар. 2014 г. · There are at least two ways: Computing √ 10 , then the square root of it, etc. until the result is small enough to do an approximation.

10 окт. 2014 г. · Consider α=loga and β=logb, b>a. Are there formulas for approximating γ=log(a+b)? What about θ=log(a−b)?

22 авг. 2020 г. · By Taylor series expansion we have log(1+y)≈y for small y and thus log(x(t)x(t−1))=log(x(t−1)+Δ(x(t−1))x(t−1))=log(1+Δ(x(t−1)x(t−1))≈Δ(x(t−1)x(t ...

21 мар. 2016 г. · A fast (and quite rough) approximation is a decimal logarithm is minus a number of zeros in front of your number (including the one before the decimal point).

15 сент. 2011 г. · A better approximation for the logarithm of a factorial can be found by using logn!≈nlogn−n. Interestingly, the additional terms in the ...

1 дек. 2014 г. · The Padet approximant is of the form log(1+x)≈x1+x/2 as noted by other posters. This partially explains why x√1+x is a good approximation, what ...

27 окт. 2018 г. · Since log1/x=−logx, an approximation for very small x would be the same as an approximation for very large x.

20 мар. 2024 г. · As example θ(x)=xf1(x1x) is practically the logarithm function when x>0.65 (in my humble opinion: the max difference is less than 0.0011).