2. EXPANDING AND CONDENSING LOGARITHMS

3. PROPERTIES OF LOGARITHMS Product Property: Quotient Property: Power Property: PROPERTIES OF LOGARITHMS

4. Product Property: PROPERTIES OF LOGARITHMS

5. = log a M + log a N EX. EXPRESS AS A SUM OF LOGARITHMS. 1) log a MN = log b A + log b T 2) log b AT = log M + log A + log T + log H 3) log MATH

6. = log 5 (193) EX. EXPRESS AS A SINGLE LOGARITHM 4) log 5 19 + log 5 3 5) log C + log A + log B + log I + log N = log CABIN

7. ON YOUR OWN  Expanding the Logarithm (Write as a sum of logarithms):

8. ON YOUR OWN  Expanding the Logarithm (Write as a sum of logarithms):

9. EX. EXPRESS AS A SUM OF LOGARITHMS, THEN SIMPLIFY. 6) log 2 (416) = log 2 4 + log 2 16 = 6 = 2 + 4

10. EX. 7 USE LOG 5 3 = 0.683 AND LOG 5 7 = 1.209 TO APPROXIMATE… log 5 (21) = log 5 3 + log 5 7 = 0.683 + 1.209 = 1.892 = log 5 (3 7)

11. PROPERTIES OF LOGARITHMS Quotient Property PROPERTIES OF LOGARITHMS

12. EX. EXPAND (EXPRESS AS A DIFFERENCE) 8) 9)

13. ON YOUR OWN  Expanding the Logarithm (Write as a difference of logs):

14. ON YOUR OWN  Expanding the Logarithm (Write as a difference of logs):

15. EX. 10 USE LOG 5 3 = 0.683 AND LOG 5 7 = 1.209 TO APPROXIMATE… = log 5 3 – log 5 7 = 0.683 – 1.209 = -0.526

16. PROPERTIES OF LOGARITHMS Power Property: PROPERTIES OF LOGARITHMS

17. = -5 log b 9 EX. EXPRESS AS A PRODUCT. 11) 12)

18. ON YOUR OWN  Expanding the Logarithms:

19. ON YOUR OWN  Expanding the Logarithms:

20. EX. 13 USE LOG 5 3 = 0.683 AND LOG 5 7 = 1.209 TO APPROXIMATE… = log 5 7 2 = 2(1.209) = 2.418 log 5 49 = 2 log 5 7

21. EX. 14 EXPAND = log5+ logy+ logx 3 = log5 + logy + 3 logx log5x 3 y

22. EX. 15 EXPAND Simplify the division. Simplify the multiplication of 4  Change the radical sign to an exponent Express the exponent as a product

23. ON YOUR OWN  Expanding the Logarithms:

24. ON YOUR OWN  Expanding the Logarithms:

25. EX. CONDENSE. 16) 17)

26. Express all products as exponents Simplify the subtraction. Change the fractional exponent to a radical sign. Simplify the addition. EX 18 CONDENSE

27. PROPERTIES OF LOGARITHMS log a 1 = 0 log a a = 1 log a a x = x If log a x= log a ythen x = y because a 0 = 1 because a 1 = a Change-of-Base Product Property Quotient Property Power Property