Exponential And Logarithmic Functions Page 2
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1
2
3
43.
Evaluate without a calculator. Give exact answers, whenever possible.
(a) log
(b) log 100,000,000
(c) log
1
64
3
2
Calculator Keys:
Common logarithm
LOG = log
Natural logarithm
LN
= log
10
e
4.
Evaluate. Use your calculator to approximate these to 4 decimal places.
(a) log 153
(b) log 0.0005
(c) ln 44
Solving logarithmic equations:
↔
Use
(1) changing forms
or
(2) log
u = log
v
u = v
a
a
5.
Solve for x. Give exact answers, if possible.
+
=
=
2x
x
3
(a) log
x = 10
(b)
e
5
(c)
10
10,000,000
3
“Log Rules”
M ⋅ N = log
1
5. log
M + log
N
1. log
b = 1 because b
= b
b
b
b
b
⋅ b
M
N
M + N
since b
= b
0
M
2. log
1 = 0 because b
= 1
6. log
= log
M – log
N
b
b
b
b
N
M
b
M – N
since
= b
N
b
( )
n
n
n
p
= p ⋅ log
3. log
b
= n because b
= b
p
M
M⋅p
7. log
M
M since b
= b
b
b
b
log
n
4. b
= n because log
n = log
n
log a M
b
8. log
b
b
M =
b
log a b
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