Logarithm Properties

Four hundred years ago, astronomers multiplied enormous numbers by hand — a slow, error-prone ordeal. Then John Napier had an idea that cut their workload in half: turn multiplication into addition. His trick was the logarithm. Because logs convert products into sums, you could look up the log of each number, ADD (easy), and convert back. It saved astronomers years of labor — literally, Kepler used logs to crack planetary motion. The three properties behind that magic still power computation today.