Intro to Logarithms Worksheet Properties of Simple Logarithms

Intro to Logarithms Worksheet

Properties of Simple Logarithms

loga 1 = 0 loga a = 1 loga ax = x and aloga x = x (inverse property) If loga x = loga y then x = y

Properties of Natural Logarithms

ln1 = 0 ln e = 1 ln ex = x and eln x = x If ln x = ln y then x = y

(inverse property)

A standard logarithm can have any positive number as its base except 1, whereas a natural log is always base e . Since the natural log is always base e , it will be necessary to use a calculator to evaluate natural logs unless one of the first three examples of the properties of natural logs is used. For anything such as ln 2 = , a calculator must be used.

When dealing with logarithms, switching between exponential and Logarithmic form is often necessary.

Logarithmic form loga b = c

Exponential Form ac = b

Write each of the following in exponential form.

1) log4 16 = 2

2)

log9

3

=

1 2

3)

log9

27

=

3 2

4)

log4

1 16

=

- 2

Write each of the following in logarithmic form.

5) 34 = 81

6) 161 4 = 2

7) 36-1 2 = 1 6

8) 165 4 = 32

Simplifying Logarithms

Evaluate each of the following logarithms without the use of a calculator. Remember to write in exponential form to help if needed.

9) log3 81 =

10)

1 log4 2 =

11) log12 144 =

12)

1 log6 36 =

13)

log 2

3

9 4

=

14) log0.25 4 =

15) log3-3 =

16) log8 4 =

17)

log81

1 27

=

18) log 1 32 =

16

19) log4 0 =

20) log10 1 =

21)

log4

1 8

=

22)

log27

1 3

=

23) log9 3 =

24) log6 63x =

25)

log36

1 6

=

26) log128 2 =

27) log1 16 =

4

28) logz z2x =

29) ln e12 =

30) 3log3 5 =

31) ln1 =

32) eln 4x =

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