1. 7.4 Logarithms p. 499 What you should learn: Goal1 Goal2 Evaluate logarithms Graph logarithmic functions 7.4 Evaluate Logarithms and Graph Logarithmic Functions A3.2.2

2. Evaluating Log Expressions We know 2 2 = 4 and 2 3 = 8 But for what value of y does 2 y = 6? Because 2 2 < 6 < 2 3 you would expect the answer to be between 2 & 3. To answer this question exactly, mathematicians defined logarithms.

3. Log form Exp. form log 2 16 = 4 log 10 10 = 1 log 3 1 = 0 log 10.1 = -1 log 2 6 ≈ 2.585 2 4 = 16 10 1 = 10 3 0 = 1 10 -1 =.1 2 2.585 = 6

4. Evaluate without a calculator log 3 81 = Log 5 125 = Log 4 256 = Log 2 (1/32) = 3 x = 81 5 x = 125 4 x = 256 2 x = (1/32) 4 3 4 -5

5. Evaluating logarithms now you try some! Log 4 16 = Log 5 1 = Log 4 2 = Log 3 (-1) = (Think of the graph of y=3 x ) 2 0 ½ ( because 4 1/2 = 2) undefined

6. You should learn the following general forms!!! Log a 1 = 0 because a 0 = 1 Log a a = 1 because a 1 = a Log a a x = x because a x = a x

7. Natural logarithms log e x = ln x ln means log base e

8. Common logarithms log 10 x = log x Understood base 10 if nothing is there.

9. Common logs and natural logs with a calculator log 10 button ln button