structural:reformatting
Efficient computation

For ln (x) {\displaystyle \ln(x)} where x > 1, the closer the value of x is to 1, the faster the rate of convergence of its Taylor series centered at 1. The identities associated with the logarithm can be leveraged to exploit this: ln 123.456 = ln (1.23456 ⋅ 10 2) = ln 1.23456 + ln (10 2) = ln 1.23456 + 2 ln 10 ≈ ln 1.23456 + 2 ⋅ 2.3025851. {\displaystyle {\begin{aligned}\ln 123.456&=\ln(1.23456\cdot 10^{2})\\&=\ln 1.23456+\ln(10^{2})\\&=\ln 1.23456+2\ln 10\\&\approx \ln 1.23456+2\cdot 2.3025851.\end{aligned}}}

Such techniques were used before calculators, by referring to numerical tables and performing manipulations such as those above.