We look at the origins of a logarithm.

### Why would someone care about logarithms?

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.**

### How does the logarithm work?

Still thinking about our work above, consider this: If we want a function to have the property then how is a logarithm actually defined?

**natural logarithm**is the accumulation function defined by The domain of the natural logarithm is (all positive real numbers), and its range is (all real numbers).

Finally, we’ll show that the natural logarithm has the property that transforms multiplication into addition.