PROPERTIES OF LOGARITHMSLegac Algebra 2
NAME _
r--- 1. Product Property
2. Quotient Property
3. Power Property
EXPAND h Ii IIt e o owmg expressions1.
Jogsxy2.
logi3.
,logg.Y?
»:4.. Jog! 5. log36xy 6. 1 4 Iogr
-
7. 6 8. 4; 9. logfYlog Y logsX
r-:
10.logf
11. log63fi.? 12. xlog3 '4
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r
b. I -,yyjf:(}SF. .*- rinG') '1cv~-13 .. logr + log2Y 14. 3 logzr - log2Y 15. 4 log x + 3 Jogx
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16. logs8 + logsx 17. log313 + log33 18. log42 - log46
19. 2logx + logS 20. log216 - log28 21 '• logsx + 3 logsY
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i ,
-
22. log 2 - 210gx 23. 3logr - 5log7y24. 3 log33 - log33
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25. I 3 26. logs6 - logs4 : 27. Y:l\00)(+~lo9~-2\~"l:og2 + 4 Jogzr
28. \~ l-\og 3+ log6 29. 2109/\-3Io~~ 30. 21~'f..-3\C0~ + 4\~r
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Name Class Date _
t ' ..- BacKSfde1. about 377.7 decibels 2. about 2.6 decibels 3.1.07924.1.2042 5. -0.2219 6. -0.0969 7. 1.8751 8. 0.50529.0 10.1.7782 11.logs12 12.log65 13.logz1 = 0
2 1 114. log~ 15.log415x 16. log 14 17. log x3 18.logr!f
.y . 14
19.1og3100xT 20.log.8 21; log 3.~ .22. log 64. 23. logi24. log xII i 25.log6!.2,6. log ~ 27 .logj ~~
1 ~ 1 .xJ x-y! . .?4 Y .28.log21 29. log -2- 30. log t: 31. logs48yJ Z .r t
32. log x + log Y + log z 33. logzt' - logzy - log2z34. log 6 + 3 log x + logy 35. log 7 + 2 log (3x - 2)
. 36 1 I 1 1· 1 1 1. ·z og2 + Z/ogr + zlogs + zlogl - zlog5 - zlogw37. log 5 + logx - log 4 - logy38.logs5 - 5 l~gsX'or 1 - 5 logsX .39. log 2 ,+2 log x + 10gy -. log 3 ....,3 log k I
40. 2log43 + 2log.r -+ 2log~ + 2log4z 41. Quotient IProp. 42. Power Prop. 43. Product Prop. 44. Power Prop. !]45. Power Prop. 46. Power and Quotient Prop. .
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E~ampJes'Expand log23x4.
log23x4 = log23 + log2x4 = log23 + 4 log2x
.~~ing8-41. log 2 - log 3 2. log 6 + log y3~log 1 - log 5, or .-log 5 4. 3 logr5. log36 + logr+ log~6.log636 + 2log6x, or 2 + 2log6x 7.logsX + logsY8.logr - log34 9.4logr 10. 2logr + log~ v
11.71oggY 12. 4logsX + 3logsY 13.log339 14. log 5i!. 1 .
15.log43' 16. log39,or 2 17.logs8x 18. log-1." x2
1 x3 79.lo~y ?O.lo~ys. 2.1.logx 22. logs xy3
x323. lo~y 24. lo~ 2, or 1
Use properties of logarithms to expand the following expressions.
1. 2 2. log 6ylog '3 '
3. log~ 4. log3x3
5. log36xy 6. log636x2
7. logsxy 8. log3 t9. log7x4 10. log3~y
11. loggY7 12. logsx4y3
(ij::cQ)oE!!:0..co'"~Q)0..
'"caClcz Use properties of logarithms to write each logarithmic expression as a.!!1:g single logarithm.Q.
ooSco~o:>"CLlJco~caQ)0..
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13. log313 + log33 14. 2 log x + log 5
15. log42 - log46 16. 3 log33 - log33
17. logs8 + logsx 18. log 2 - 2 log x
19. log2x + log2Y 20. :3 log7x - 5 log7Y
21. 4 log x + 3 log x 22. logsx + 3 logsY
23. 3 log2x - log2Y 24. log216 - log28
Name Class Date _
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Properties of Logarithms
For Exercises 1-2, use the formula L = 10 log II., 0 "1. A sound has an intensity of 5.92 X 102SW/m2. What is the loudness of
the sound in decibels? Use 10 = 1O-12Wjm2.
2. Suppose you decrease the intensity of a sound by 45%. By how manydecibels would the loudness be decreased?
Assume that log 3 = 0.4771, log 4= 0.6021, and log 5 = 0.6990. Use theproperties of logarithms to evaluate each expression. Do not use it calculator.
3. log 12 4. log 16
8. log \67. log 75
5. log ~
9. log61 - log 1
Write each logarithmic expression as a single logarithm.
11. logs4 + logs3
14. 5 log7x - 2 log7x
17. 2 log x - 3 log Y
20. 5 log 2 - 2 log 2
23. (log 3 - log 4) - log2
26. log 2 + log 4 - log 7
29. !log x + t log y - 2 log z
Expand each logarithm.
32. log xyz
35. log 7(3~ - 2)2
12. log625 - log65
15. log460 - log44 + log4x
18. !log T + t log s - i log t
21. t log 3x + ~ log 3x
24. 5 log x + 3 log ~
27. log32x - 5 log}y
30. 3(4 log (2)
"33: log2 ;z36. log ~t!t
2x2y39. log 3k3
State the property or properties used to rewrite each expression.
41. log 6 - log 3 = log 21 .•31
44. 3" logzX = log2 \I x
42. 6 log 2 = log 64
45. ~log7 = log~
6. log 0.8
10. log 60
13. log24 + log22 - log28
16. log 7 - -log 3 +.log 6
19. log34x + 2 log35y
22. 2 log 4 + log 2 + log 2
25. log63 - log66
28. t(log2x - log2Y)
31. logsY - 4(lOgsT + 2 logst)
1 5x37. og 4y
40. log4(3xyz)2
,, I
43. log 3x = log 3 + log.x" "20
46. log420 - 3 log4x = log4"3x
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