1. I CAN APPLY PROPERTIES OF LOGARITHMS

2. Warm-up Can you now solve 10 x – 13 = 287 without graphing? x ≈ 2.48

3. Properties 1.log b (xy) = log b x+ log b y 2.log b (x/y) = log b x – log b y 3.log b x p = p log b x Let’s prove 1 and 3 now.

4. Examples  1.Simplify completely. a)log 10 50 + log 10 2 b)log 8 56 – log 8 7 c)log 2 5 √16 d)5 ln e 2 – ln e 3 Answers: a)2b)1 c)4/5d)7

5. Examples  2.Write as a single log (condense) ½ log b x – log b (1 + x 2 )  Answer:log b √x 1+x 2

6.  3.Write as the sum or difference of logs (expand).

7.  Answer: 1/3[log 10 2 + log 10 x – log 10 (3x 2 + 1)]

8.  4.Write each expression in terms of ln 2 and ln 3. a)ln 54 ln 2 + 3 ln 3 b)ln (9/8) 2 ln 3 – 3 ln 2

9.  Solve 2 x = 3 Take the log of both sides. log 2 x = log 3 x log 2 = log 3 (property 3) x = log 3/log 2 ≈ 1.58 Note that the equation is equivalent to log 2 3=x, so log 2 3 = log 3/log 2…

10. Base Change Formula log b x = log a x/log a b In most cases you will let a be 10 or e so that you can use your calculator to evaluate.

11. Estimate the value of log 5 75. Evaluate log 5 75 using the base change formula. Answer: ≈ 2.68

12. Solve 5∙ 7 x = 100 log 7 20 = x x≈ 1.54

13. THE END