Aim: What are the properties of logarithms? Do Now: Rewrite the following exponential form into log form 1.b x = A 2.b y = B HW:p.331 # 16,18,20,22,24,26,28,38,40,42,48,52 Replace x and y by log b A and log b B log b AB = log b b x + y

Product Rule: log b AB = log b A + log b B Quotient Rule: log b A/B = log b A - log b B Power Rule: log b A c = c log b A RULES of LOGARITHMS

Example 1. Find the value of log log 6 3 use the product rule log 6 (12·3) simplify = log 6 36 Write it as exponential equation 6 a = 36 Evaluate a = 2

2. If 2 log log 2 x = log 2 27, find x Simplify left-hand side. Use the power rule, then use the product rule log log 2 x = log 2 27 log 2 (9 2 · x) = log 2 27 log 2 (81x) = log 2 27 Equate the powers, and solve for x 81x = 27

3. If express log 10 x in terms of log 10 a and log 10 b Express as a power Write the log to the base 10 of each side the equation Use the quotient rule Use the power rule

4. The expression log 3 a 5 b is equivalent to a)5 log 3 ab b) 5 log 3 a + log 3 b c) log 3 5ab d) log 3 5a + log 3 b Use the product rule log 3 a 5 b = log 3 a 5 + log 3 b Use the power rule = 5 log 3 a + log 3 b

1. Write the expression in terms of log 10 a and log 10 b a.log 10 ab b.log 10 (a 2 b) 2. Solve for n: 3 log 2 4 = log 2 n 3. Solve for n: log – 2 log = log 5 n a. log 10 a + log 10 b b. 2 log 10 a + log 10 b 64 1/10 or 0.1