1. Quiz 3.2

2. 3.3 Properties of Logarithms Date: ____________

3. Change of Base Theorem log a x= log x log a log a x= ln x ln a OR

4. 1) 2)

5. 1) 2)

6. Evaluating Logarithms log 5 23= log23 log5 ≈ 1.948 OR log 5 23= ln23 ln5 ≈ 1.948

7. Other Examples log 3 149= log149 log3 ≈ 4.555 log 7 300= log300 log7 ≈ 2.9312

8. Properties of Logarithms Product Property Quotient Property Power Property Let b, u, and v be positive numbers such that b ≠ 1. log b uv = log b u + log b v log b u n = nlog b u log b = log b u − log b v u v

9. 1) 2) 3)

10. 1) 2) 3)

11. Find the exact value of the logarithm.

12. Use the properties of logarithms to simplify the given expression.

15. Write as the sum, difference, or product of logarithms. Simplify, if possible. log 4 4x64x6 y =log 4 4x 6 – log 4 y = log 4 4 + log 4 x 6 – log 4 y = log 4 4 + 6log 4 x – log 4 y = 1 + 6log 4 x – log 4 y

16. Write as the sum, difference, or product of logarithms. Simplify, if possible. log 7 6 x3yx3y =log 7 6 – log 7 x 3 y = log 7 6 −(log 7 x 3 + log 7 y) = log 7 6 − (3log 7 x + log 7 y) = log 7 6 − 3log 7 x − log 7 y

17. Write as the sum, difference, or product of logarithms. Simplify, if possible. log 5 7 x= log 5 7 + log 5 x = log 5 7 + log 5 x ½ = log 5 7 + ½log 5 x

18. Write as the sum, difference, or product of logarithms. Simplify, if possible. log a x3y5x3y5 z = log a x3y5x3y5 z ½ = ½ log a x3y5x3y5 z = ½( log a x 3 + log a y 5 – log a z) = ½(3 log a x+ 5log a y – log a z)

19. Condense the expression to the logarithm of a single quantity. log 3 5 + 6log 3 x − log 3 7 = log 3 5 + log 3 x 6 − log 3 7 = log 3 (5x 6 ) − log 3 7 = log 3 7 5x 6

20. Condense the expression to the logarithm of a single quantity. 3log 8 x − 5log 8 y + log 8 15 = log 8 x 3 − log 8 y 5 + log 8 15 15 log 8 y5y5 = x3x3 = log 8 y5y5 15x 3

21. x3x3 Condense the expression to the logarithm of a single quantity. 3log 8 x − 5log 8 y − log 8 15 = log 8 x 3 − log 8 y 5 − log 8 15 = log 8 15y 5