1. Properties of logarithms

2. Properties of Logarithms Let b, u, and v be positive numbers such that b≠1. Product property: log b uv = log b u + log b v Quotient property: log b u/v = log b u – log b v Power property: log b u n = n log b u

3. Use log 5 3≈.683 and log 5 7≈1.209 Approximate: log 5 3/7 = log 5 3 – log 5 7 ≈.683 – 1.209 = -.526 log 5 21 = log 5 (3·7)= log 5 3 + log 5 7≈.683 + 1.209 = 1.892

4. Use log 5 3≈.683 and log 5 7≈1.209 Approximate: log 5 49 = log 5 7 2 = 2 log 5 7 ≈ 2(1.209)= 2.418

5. Practice In small groups work on pg. 441 #3-13 odd

6. Expanding Logarithms You can use the properties to expand logarithms. log 2 = log 2 7x 3 - log 2 y = log 2 7 + log 2 x 3 – log 2 y = log 2 7 + 3·log 2 x – log 2 y

7. Your turn! Expand: log 5mn = log 5 + log m + log n Expand: log 5 8x 3 = log 5 8 + 3·log 5 x

8. Condensing Logarithms log 6 + 2 log2 – log 3 = log 6 + log 2 2 – log 3 = log (6·2 2 ) – log 3 = log = log 8

9. Your turn again! Condense: log 5 7 + 3·log 5 t = log 5 7t 3 Condense: 3log 2 x – (log 2 4 + log 2 y)= log 2