Explain the log 1 = ? Don’t forget that……. 1

2 Algebra 2: Section 8.5 Properties of Logarithms

Remember when….. Product Property Quotient Property Power Property 3

4 Properties of Logarithms 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

5 Examples Use log g 5 ≈ and log g 11 ≈ to approximate the following. 1.log g (5/11) log g 5 – log g =

Examples (continued) 2.logg55 = logg5(11) = logg5 + logg11 = = log g 25 = log g 5 2 = 2(log g 5) = 2(0.732) =

7 Examples Expand the expressions. 4.log 5 2x 6 log log 5 x 6 log (log 5 x)

8 Examples (Expand - continued) 5.log 3xy 3 = log(3) + log(x) + log(y 3 ) = log(3) + log(x) + 3log(y) 6.ln (10/3) = ln10 – ln 3

Examples (Expand - continued) 9

10 Homework p.496 #22-44 evens

11 Algebra 2: Section 8.5 Properties of Logarithms (Day 2)

12 Properties of Logarithms Product Property log b u + log b v = log b uv log b u + log b v = log b uv Quotient Property log b u – log b v = log b (u/v) log b u – log b v = log b (u/v) Power Property n log b u = log b u n n log b u = log b u n

13 Examples Condense the Expressions 7.2 log37 – 5 log3x = = =

14 Examples (Condense - continued) 8. ln 20 – ln 4

(log 7 18 – log 7 9) + 2 log 7 (1/2)

16 Change of Base Formula (Yesterday) Used to evaluate logs that are bases other than 10 or e.

17 Examples Use the change of base formula to evaluate the expression. 10. log log 6 15

18 Homework p.496 #46-68 evens