Exponential And Logarithmic Equations Worksheet - Section 4-7 Page 6
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4-7 Exponential and Logarithmic Equations
2
2
Solve log x
(log x)
.
M A T C H E D P R O B L E M
6
Note that
C A U T I O N
2
(log
x)
(log
x)(log
x)
b
b
b
2
2
(log
x)
log
x
2
log
x
2 log
x
b
b
b
b
E X A M P L E
Earthquake Intensity
7
Recall from Section 4-6 that the magnitude of an earthquake on the Richter
scale is given by
2
E
M
log
3
E
0
Solve for E in terms of the other symbols.
2
E
M
log
S o l u t i o n
3
E
0
E
3M
3
Multiply both sides by .
log
2
E
2
0
E
3M/2
Change to exponential form.
10
E
0
3M/2
E
E
10
0
Solve the rocket equation from Section 4-6 for W
in terms of the other symbols:
M A T C H E D P R O B L E M
b
7
W
t
v
c ln
W
b
Change of Base
How would you find the logarithm of a positive number to a base other than 10
or e? For example, how would you find log
5.2? In Example 8 we evaluate this
3
logarithm using a direct process. Then we develop a change-of-base formula to
find such logarithms in general. You may find it easier to remember the process
than the formula.
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