1. P ROPERTIES OF L OGARITHMS Unit 3C Day 3

2. D O N OW Condense: 3log 2 x – (log 2 4 + log 2 y )= Expand: log 5 (8 x 3 ) = Also, take a calculator.

3. S PECIAL L OGARITHMS A common logarithm is a logarithm with base ____ Instead of writing log 10 x, we usually just write __________ A natural logarithm is a logarithm with base ____ Instead of writing log e x, we usually just write ___________ It comes from the Latin “logarithmus naturalis.”

4. E X. 1: U SING THE C ALCULATOR TO E VALUATE L OGS Evaluate the following. a) log 8 b) ln 0.3 c) log 1000 d) ln 1

5. U SING THE C ALCULATOR TO E VALUATE L OGS How could we use the calculator to evaluate a log with a base other than 10 or e ? Say we want to find y = log c a ( a and c are positive with c ≠ 1)… Change of base formula:

6. E X. 2: C HANGE OF B ASE F ORMULA Use the change of base formula to evaluate: a) log 3 7 = b) log 6 11 = c) log 16 26 = d) log 5 13 =

7. C LOSURE What is the purpose of the change of base formula? What is the actual formula?