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.

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.

anonymous · Answer

the sum of the logarithms is equal to the logarithm of their product