1. PROPERTIES OF LOGARITHMS
LESSON 10 – 2
MATH III

2. Logarithms vs. Exponents
Logarithms represent exponents. This makes the rules identical. x4 * x3 x5 x2

3. Examples
Log (x2y4) Log2 (x5y2) Log x2 y3 Log3 x2y3 z5

4. Condensing
4logx – 5logy 2logx + 6logy 12log3x – (4log3y + 2log3z) (3logx + 3logy) – 5logz

5. Solving Log Equations
Logarithms kill exponents. Ex: 4x = 72 Ex: 3(5x) = 108 Ex: 4(2x) + 7 = 167 Ex: 103x-1 = 28

6. Solving Log Equations
Exponents kill logarithms. Ex: log5(x + 8) = 2 Ex: log3(3x – 2) = 4 Ex: log6(x) log6(x-5) = 2

7. Logs on Both Sides Cancel
log(11x – 3) = log(9x + 17) log3(2x – 1) = log3(4x – 37) log6(4) + log6(x + 2) = log6(80) log3(x) + log3(x + 5) = log3(66)