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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