1. 5.3.1 – Logarithmic Functions

2. When given exponential functions, such as f(x) = a x, sometimes we needed to solve for x – Doubling time – Years to reach a particular amount Trouble is, we don’t have an exact way to solve for x

3. Log Function Luckily, we can use a logarithmic function to help us solve such problems If a is a fixed positive number, and if x = a y, then; – y = log z x – a is the bsae of both functions/equations OR, a to what power gives you x

4. Properties There are some simple properties we can use to help us better understand logs Log a 1 = 0 – Why? Log a a = 1 – Why?

5. Properties Cont’d Log a (a x ) = x (Knockdown Property) a loga(x) = x If no base is listed, we assume base 10

6. Example. Evaluate the following logarithmic expressions: a) log 5 25 b) log 1/2 2 c) log 17 1

7. Try these D) log 16 4 E) log 3 1 F) log 5 (1/25) G) 2log 9 81

8. Assignment Pg. 411 13-23 odd