Question

In the days before affordable calculators were available, students learned to multiply large numbers using the following technique:

1. Find the common logarithm (base 10) of each number, usually from a book containing tables of logarithms.
2. Add the logarithms.
3. Look at the table to find the number that had the sum for a logarithm.

Explain why it makes sense that you could find the product of two numbers by adding their logarithms.