1. logb AB = logbbx + y Aim: What are the properties of logarithms?
Do Now: Rewrite the following exponential form into log form
bx = A
by = B
logb AB = logbbx + y
Replace x and y by logbA and logbB

2. RULES of LOGARITHMS Product Rule: logb AB = logb A + logb B
Quotient Rule: logb A/B = logb A - logb B
Power Rule: logb Ac = c logb A

3. Example 1. Find the value of log6 12 + log6 3 log6 (12·3)
use the product rule
= log6 36
simplify
Write it as exponential equation
6a = 36
Evaluate
a = 2

4. 2. If 2 log2 9 + log2 x = log2 27, find x
Simplify left-hand side .
Use the power rule,
then use the product rule
log log2 x = log2 27
log2 (92 · x) = log2 27
log2 (81x) = log2 27
Equate the powers,
and solve for x
81x = 27

5. 3. If express log10 x in terms of log10 a
and log10 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

6. 4. The expression log3 a5b is equivalent to
5 log3 ab b) 5 log3 a + log3 b
c) log3 5ab d) log3 5a + log3 b
Use the product rule
log3 a5b = log3 a5 + log3 b
Use the power rule
= 5 log3 a + log3 b

7. 1. Write the expression in terms of log10 a and log 10 b
log10 ab
log10 (a2b)
a. log10 a + log10 b
b. 2 log10 a + log10 b
2. Solve for n: 3 log2 4 = log2 n 64
3. Solve for n: log – 2 log5 100 = log5 n
1/10 or 0.1