Properties of Logarithms - Kuta Software

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 )

-1-

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

-2-

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

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-2-

Worksheet by Kuta Software LLC

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