Basic Logs

*Logarithmic Functions are the inverse of Exponential functions. So if you have the points (4,16) on an Exponential Graph, the points would be (16,4) on a Inverse Logarithmic Graph.

Logarithmic Equations look like this = LogaU=X

Another way of writing this logarithm is: ax= U

*The two most important common Logarithms are the common logarithm (LOG) and the Natural Logarithms (LN) Common Logs have a base of 10 and Natural Logs have a base of e.

    *There are three important Log rules

        1. Loga (UV) = Loga (U) + Loga (V)

        2. Loga (U/V) = Loga (U) - Loga (V)

        3. Loga (U)n = n*Loga (U)

Examples:

1. Log525 + Log5125 = Log5(125*25) =Log53125=5

2. Log5125- Log525 = Log5(125/25)=Log55=1

3. Log510^x= x*Log510

            -Let "a" be a positive number, a not equal to 1, Let "n" be a real number and let "u and v" be positive real numbers.

            -The reason for these rules are for future problems. If you get a problem that looks similar to one of the equations listed above, then you plug in your numbers into that equation and you will find your answer.

    *Examples

        -Exponential Equation- 4^3 = 64 as a Log- log4 (64) = 3

        -Exponential Equation- 5^-2 = 1/25 as a Log- log5 (1/25) = -2

Check: You can check your answer in two ways. You could graph the function Ln(x)-8 and see where it crosses the x-axis. If you are correct, the graph should cross the x-axis at the answer you derived algebraically.

You can also check your answer by substituting the value of x in the initial equation and determine whether the left side equals the right side. For example, if Ln(2,980.95798704)=8, you are correct. It does, and you are correct.