# Design Scheme Assignment

## How logarithms work

### What is a logarithm?

The logarithm is the inverse of exponentiation. It involves a base number, which is the same base used with exponents but the result of a logarithm is the exponent that would be raised to that base and the result of exponentiation is equal to the input of the logarithm.
Example: log base 10 of 100 is 2, just as 10 to the power of 2 is 100

### How are logarithms added or subtracted with the same base?

If two logarithms have the same base, then they may be added or subtracted to be combined using multiplication and division.
Example: Log base10 of 10 + Log base10 of 100 is equal to Log base10 of 100 * 10 or Log base10 of 1000, which is 3

### How are inputs with exponents related with their base?

If a logarithm has an input to a exponent when the input is equal to the base, then the logarithm is equal to the exponent.
Example: Log base10 of 10 to the third power is equal to 3 because the input of 10 is raised to an exponent of 3