4.4 Expanding and Condensing Logarithms - Amphitheater Public Schools

Algebra 2

Name___________________________________

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4.4 Expanding and Condensing Logarithms

Date________________ Period____

Expand each logarithm.

( )x4 6

1) log y

2) log (z2 x) 5

3) log (x4y3) 5

4) log 6 (ab3)2

( )62 2

5) log 7

6)

log

4

(6 ? 72)3

( )114 2

7) log 78

8) log (x y )5 6 9

Condense each expression to a single logarithm.

9) 5 log 11 + 10 log 6

3

3

1 10) 6 log 9 z + 2 ? log 9 x

1 11) 3 log 4 z + 3 ? log 4 x

1

1

12)

log

6

c +

2

? log 6

a +

2

? log 6

b

13) 6 log 2 + 24 log 7

5

5

14) 30 log x + 6 log y

4

4

15) 16 log a - 4 log b

4

4

16) log x + log y + 4 log z

5

5

5

Worksheet by Kuta Software LLC ?w T2X0v1^8] lKeultFaX qSaomfSt`wMaErveW KLYL\C[.E F nACltlC Jr]ikgShatZsc Grle]s[eKrNveeLdy.F w CMTaZdReb iwvihtzhc PIZnJfRiUnEidtJen kAHlzgEeDb_rvaG V2_.

Algebra 2

Name___________________________________

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4.4 Expanding and Condensing Logarithms

Date________________ Period____

Expand each logarithm.

( )x4 6

1) log y

24 log x - 6 log y

2) log (z2 x) 5

1

2 log z + ? log x

52

5

3) log (x4y3) 5

4 log x + 3 log y

5

5

( )62 2

5) log 7

4 log 6 - 2 log 7

4) log 6 (ab3)2

2 log 6 a + 6 log 6 b

6)

log

4

(6 ? 72)3

3 log 4 6 + 6 log 4 7

( )114 2

7) log 78

8 log 7 11 - 2 log 7 8

8) log (x y )5 6 9 6 log 9 x + 30 log 9 y

Condense each expression to a single logarithm.

9) 5 log 11 + 10 log 6

3

3

( ) log 3 610 ? 115

1 10) 6 log 9 z + 2 ? log 9 x

log (z6 x) 9

1 11) 3 log 4 z + 3 ? log 4 x

log 4 (z3 3 x)

1

1

12)

log

6

c +

2

? log 6

a +

2

? log 6

b

log 6 (c ba)

13) 6 log 2 + 24 log 7

5

5

( ) log 5 724 ? 26

14) 30 log x + 6 log y

4

4

( ) log 4 y6x30

15) 16 log a - 4 log b

4

4

a 16 log

4 b4

16) log x + log y + 4 log z

5

5

5

log 5 ( yxz4)

Worksheet by Kuta Software LLC ?G q2^0p1V8x `KAuNtuah ASHoFfAtuwOaArZeB qLoL^CS.F E FA]lvl[ trjiCgyhvtIsU JrOeBsueHrAveeAdz.o z MMzaBdgem ]wgikt^hB QIZnLfDiznOirtSen zAelAgKeHbUrqa_ h2U.

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