[PDF] [PDF] Logarithms Expand, Condense, Properties, Equations

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Properties for Expanding Logarithms 0 log 1 = or a log 10 = This is property number 1 which says that log of 1 will always equal zero no matter what the base is If we went through and rewrote each of the properties of exponents we would get the properties of logarithms shown above

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E f OAwlTl3 0r3i1gHhntwsG SrPeCsMeHruvQekds G Expanding and Condensing Logarithms Condense each expression to a single logarithm 1) 3log 9

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[PDF] Logarithms Expand, Condense, Properties, Equations

Worksheet by Kuta Software LLC Voluntary Worksheet Logarithms: Expand, Condense, Properties, Equations Expand each logarithm 1) ln (x 6 y 3) 2) log 8

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g q NAJlglr ZrQiQgrhRt5sQ Prfe0sre4r8v4eXdc c Expanding and Condensing Logarithms Expand each logarithm Justify each step by stating logarithm 

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Voluntary Worksheet

Logarithms: Expand, Condense, Properties, Equations

Expand each logarithm.

1) ln

x 6 y

3)2) log8(

x y z 3)

3) log9

33
7) 4

4) log7

x 3 y 3

5) log8(

a 6 b

5)6) log4(

63 ?
113)

7) log3

u 3 v

28) ln

3 u v w

9) log6(

3 ? 2 ?

56)10) log4(

2 ? 11 ?

74)

11) log6(

c 53
a

12) ln

52
2) 5

13) log5

x 3 y

614) log4(

7332)

15) log2(

u v w

2)16) log9

123 ? 7)6

17) log9(

c 53
a -1-

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18) log7

x 5 ? y )419) log7( z 2 x

20) log8(

u v w 5)

Condense each expression to a single logarithm.

21)
2log6 u 8log6 v 22)
8log5 a 2log5 b 23)

8log312 +

2log3524)

3log4 u

18log4

v 25)
2log5 z log5 x 2 26)
6log2 u

24log2

v 27)

6log8 -

30log1128)

4log911 -

4log97

29)
3log x 5log y 30)

6log610 -

24log63

31)
ln z ln x 3 + ln y 3 32)
3log4 x 9log4 y 33)
5log4 a 6log4 b 34)
log9 z log9 x 2 + log9 y 2 35)

4log211 -

6log2636)

log7 z log7 x 3 + log7 y 3 -2-

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37)
2log2 x

10log2

y 38)
log5 w log5 u 3 + log5 v 3 39)
log37 + log310 3 + log311 340)
log9 u 2 + log9 v 2 + log9 w 2

Rewrite each equation in exponential form.

41) log

17289 = 242) log981 = 2

43) log

14196 = 244) log61 = 0

45) log100 = 246) log

32
1 2 = -1 5

47) log6

1

36 = -248) log18324 = 2

49) log

27
1 3 = -1 3

50) log216 = 4

51) log

6416 =

2 3

52) log749 = 2

53) log

18 1

324 = -254) log81

1 3 = -1 4

55) log7343 = 356) log

22515 =

1 2

57) log11121 = 258) log141 = 0

59) log

327 = 360) log

32418 =

1 2 -3-

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Rewrite each equation in logarithmic form.

61)

110 = 162)

7-2 = 1 49
63)

152 = 22564)

121
-1 2 = 1 11 65)

34 = 8166)

72 = 49

67)

43 = 6468)

361
1

2 = 19

69)

73 = 34370)

11-2 =

1 121
71)

33 = 2772)

4-2 = 1 16 73)
64
1

2 = 874)

112 = 121

75)

162 = 25676)

82 = 64

77)

192 = 36178)

225
1

2 = 15

79)

12-2 =

1 144
80)
144
1

2 = 12

Solve each equation.

81) log

526 = log5

p

82) log20(

8 - 2 x ) = log20( -3 x + 10)

83) log3(

-4 x + 7) = log32 x

84) log4(

x + 6) = log4( 3 x - 6)

85) log4(

-4 x + 2) = log4( -5 x - 4)86) log93 m = log9( 2 m + 3) -4-

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87) log19(

-4 n - 2) = log19( 3 n + 5)88) log20( -4 n - 5) = log20( -3 n + 10)

89) log(

-3 b + 9) = log( -4 b - 10)90) log6( -5 r - 2) = log6( r - 4)

91) log8(

4 v - 4) = log8( 3 v - 10)92) ln( -2 k - 2) = ln( -3 k - 9)

93) log2(

-4 x - 4) = log2( x + 6)94) log63 = log6( 4 p + 3)

95) log4(

-2 x - 4) = log4( 3 x + 9)96) ln( x + 5) = ln( 7 - 2 x

97) log13(

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