A lot of people, when they hear that we are using logarithm as a trick to go from a multiplication to an addition, think that we are diverting the log from its original purpose, we are “hacking” it.

That’s what the logarithm was invented for.

In fact, the logarithm function is the ONLY (continuous) function such that f(x*y) = f(x)+f(y).

Here is what Napier, who invented/discovered the log, had to say about it in 1614:

“…nothing is more tedious, fellow mathematicians, in the practice of the mathematical arts, than the great delays suffered in the tedium of lengthy multiplications and divisions, the finding of ratios, and in the extraction of square and cube roots… [with] the many slippery errors that can arise…I have found an amazing way of shortening the proceedings [in which]… all the numbers associated with the multiplications, and divisions of numbers, and with the long arduous tasks of extracting square and cube roots are themselves rejected from the work, and in their place other numbers are substituted, which perform the tasks of these rejected by means of addition, subtraction, and division by two or three only.”