Estimating Logarithms
a year ago
- #logarithms
- #python
- #mathematics
- The book 'The Lost Art of Logarithms' by Charles Petzold discusses a method for estimating the logarithm of any number base 10, developed by John Napier around 1615.
- A simple approximation for the logarithm of a number is the number of digits minus one, which is particularly evident for numbers between 100 and 1000.
- Henry Briggs used a method involving exponentiation to compute logarithms to high precision, such as the 14th digit for logarithms of 2 and 7.
- Scientific notation simplifies the calculation of logarithms by breaking numbers into mantissa and exponent parts, making the process more manageable.
- A Python script is provided to calculate logarithms to arbitrary precision by iteratively exponentiating and adjusting the mantissa and exponent.
- The method leverages previous calculations to build precision incrementally, requiring only simple multiplications and additions for each step.
- The author recommends reading the original source material for a deeper understanding of the logarithmic techniques discussed.