1. Logarithms Common Logarithms Integer Logarithms Negative Logarithms Log of a Product Log of a Quotient Log of an Exponential Natural Logarithms

2. Common Logarithms Key Point: The common logarithm of a number (N) is an exponent (x) where 10 x = N. The general equations is log 10 N = x where 10 x = N log 10 1000 = 3 10 3 = 1000

3. Integer Logarithms Key Point: Only numbers that are powers of 10 will have logarithms that are whole numbers. log 10 = 1 log 100 = 2

4. Negative Logarithms Key Point: For any number between 1 and 0, the logarithm is a negative number. log 1 = 0 log 0.1 = ‑ 1

5. Log of a Product Key Point: Multiplication of numbers, using logarithms, is reduced to addition. The log of a product is the sum of the logs of the factors. log ab = log a + log b

6. Log of a Quotient Key Point: Division of numbers, using logarithms, is reduced to subtraction. The log of a quotient is the difference of the logs of the dividend and divisor. log a/b = log a - log b

7. Log of an Exponential Key Point: Raising a number to a power is a process of multiplication. log a x = x (log a)

8. Natural Logarithms Natural logarithms are exponents where e is the base. e  2.718. log e N is usually written as ln N ln 10 = 2.30