Logs are linearized exponents so all the laws of exponents are the log laws: log(xy) is logx + logy. Logs are also a way to scale which is what they were origin

Logs are linearized exponents so all the laws of exponents are the log laws: log(xy) is logx + logy. Logs are also a way to scale which is what they were originally used for to do large multiplication without electronic assistants. We log scale graph axis/plots all the time today. They also describe the shape of some processes hence come up in compsci like tree algos. If you have a logarithmic process and work increases by a million new inputs then actual work is only 6x increase. So log is also the number of zeros in a number There's a book called Calculus Reordered by Bressoud that describes Napier logs/natural ln(x) too