Kuta Software - Infinite Algebra 2

Name___________________________________

Properties of Logarithms

Date________________ Period____

Expand each logarithm. 1) log (6 ⋅ 11)

5

2) log (5 ⋅ 3)

4) log (3 ⋅ 2 3 )

3) log

( )

5) log

2 5

6) log

x

8) log (a ⋅ b) 2

6 11

4

7) log

y

()

6

6

4

u 9) log v

11) log

6 5

3

10) log

x⋅ y⋅z

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x y5

12) log ( x ⋅ y ⋅ z 2 )

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Worksheet by Kuta Software LLC

Condense each expression to a single logarithm. 13) log 3 − log 8

15) 4 log 3 − 4 log 8

17) log 7 − 2 log 12

14)

log 6 3

16) log 2 + log 11 + log 7

18)

2 log 7 3

19) 6 log 3 u + 6 log 3 v

20) ln x − 4 ln y

21) log 4 u − 6 log 4 v

22) log 3 u − 5 log 3 v

23) 20 log 6 u + 5 log 6 v

24) 4 log 3 u − 20 log 3 v

Critical thinking questions: 25) 2(log 2 x − log y) − (log 3 + 2 log 5)

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26) log x ⋅ log 2

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Worksheet by Kuta Software LLC

Kuta Software - Infinite Algebra 2

Name___________________________________

Properties of Logarithms

Date________________ Period____

Expand each logarithm. 1) log (6 ⋅ 11)

2) log (5 ⋅ 3)

log 6 + log 11

3) log

( ) 6 11

5

log 5 + log 3

4) log (3 ⋅ 2 3 ) log 3 + 3 log 2

5 log 6 − 5 log 11

4

5) log

2 5

6) log

4 log 2 − log 5

7) log

6

6 log 6 − 6 log 5

8) log (a ⋅ b) 2

x y

() 6 5

6

2 log a + 2 log b

log x − 6 log y

4

u 9) log v

10) log

4 log u − log v

11) log

3

x⋅ y⋅z

y5

log x − 5 log y

12) log ( x ⋅ y ⋅ z 2 )

log x log y log z + + 3 3 3

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x

log x + log y + 2 log z

-1-

Worksheet by Kuta Software LLC

Condense each expression to a single logarithm. 13) log 3 − log 8 log

3 8

3

log 6 3 log

15) 4 log 3 − 4 log 8 log

14)

3

6

16) log 2 + log 11 + log 7

4

log 154

84

17) log 7 − 2 log 12

18)

7

log

12

3

2

19) 6 log 3 u + 6 log 3 v

log 4

2

20) ln x − 4 ln y ln

x y4

22) log 3 u − 5 log 3 v

u

log 3

v6

23) 20 log 6 u + 5 log 6 v

7

log

log 3 (v 6 u 6 )

21) log 4 u − 6 log 4 v

2 log 7 3

u v5

24) 4 log 3 u − 20 log 3 v

log 6 (v 5 u 20 )

log 3

u4 v

20

Critical thinking questions: 25) 2(log 2 x − log y) − (log 3 + 2 log 5) log

26) log x ⋅ log 2

4x2 75 y 2

Can't be simplified.

Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com

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-2-

Worksheet by Kuta Software LLC