1. 4 minutes
Warm-Up
Write each expression as a single logarithm. Then simplify, if possible.
1) log6 6 + log6 30 – log6 5
2) log6 5x + 3(log6 x – log6 y)

2. 10.3 Properties of Logarithmic Functions
Objectives:
Simplify and evaluate expressions involving logarithms
Solve equations involving logarithms

3. Properties of Logarithms
For b > 0 and b  1:
Exponential-Logarithmic Inverse Property
logb bx = x
and b logbx = x for x > 0

4. Example 1
Evaluate each expression. a) b)

5. Practice Evaluate each expression. 1) 7log711 – log3 81

6. Properties of Logarithms
For b > 0 and b  1:
One-to-One Property of Logarithms
If logb x = logb y, then x = y

7. Example 2 Solve log2(2x2 + 8x – 11) = log2(2x + 9) for x.
2x2 + 8x – 11 = 2x + 9
2x2 + 6x – 20 = 0
2(x2 + 3x – 10) = 0
2(x – 2)(x + 5) = 0
x = -5,2
Check:
log2(2x2 + 8x – 11) = log2(2x + 9)
log2 (–1) = log2 (-1)
undefined
log2 13 = log2 13
true

8. Practice Solve for x. 1) log5 (3x2 – 1) = log5 2x
2) logb (x2 – 2) + 2 logb 6 = logb 6x