We look at the origins of a logarithm.
Logarithms were originally developed as a computational tool. The key fact that made this possible is that:
Before the days of calculators and computers, this was critical knowledge for anyone in a computational discipline.
Using the table again, we see that . Since we were working in scientific notation, we need to multiply this by . Our final answer is Since , this is a good approximation.
Logarithms allow us to use addition in place of multiplication.
Still thinking about our work above, consider this: If we want a function to have the property then how is a logarithm actually defined?
Finally, we’ll show that the natural logarithm has the property that transforms multiplication into addition.