Algebra 2
Introduction to Logarithms
Name____________________________________ Period___________
The Richter Scale
In the 1930’s a California seismologist, Charles Richter, developed a logarithmic scale to rate the
magnitude of an earthquake. Since then his scale has been used around the world. There are many
scales that relate the various magnitudes of an earthquake with the amplitude, time and depth of the
surface and body waves. Today we are going to examine Richter’s scale that relates the magnitude of
surface waves of an earthquake, M, and the energy, E, released in the quake. The equation is
log E 11.8 1.5M where M is the Richter scale reading. We need to learn about logarithms first before
we can use this equation.
1. Estimating with exponents.
a) 41.5 is between what two whole numbers? __________ and ________
b) 23.8 is between what two whole numbers? __________ and ________
c) 102.3 is between what two whole numbers? __________ and ________
2. Use a calculator to estimate each value of x to the nearest thousandth.
a) 10x
45
b) 10x
382
c) 10x
2
d) 10x
125
e) 10x
5488
f) 10x
62
3. Evaluate each of the following using the log button on your calculator.
a) log 45
b) log382
c) log2
d) log125
e) log5488
f) log62
4. Rewrite the Richter scale equation, log E
11.8 1.5M , as an exponential equation.
5. If the magnitude was 7.4 on the Richter scale, what amount of energy was released?
6. If the magnitude was 8.4 on the Richter scale, what amount of energy was released?
Algebra 2
Write the following in logarithmic form.
7.
8.
9.
10.
11.
12.
Write the following in exponential form.
13.
14.
15.
16.
17.
18.
Evaluate each logarithm.
19. log 4 64
20. log5 0.2
21. log 1 125
22. log36 6
5
Evaluate each logarithm using the calculator if necessary.
23. log27 3
24. log12
25. ln 6
26. ln130
Algebra 2
Definitions:
Common Logarithm – a logarithm with a base of 10. It is
denoted by log 10 or simply log .
Natural Logarithm – a logarithm with base e. It can be denoted
by log e but is more often denoted by ln .
Inverse functions
The functions g x logb x and f x
it here:
b x are inverses of each other. We can prove
Use inverse functions to simplify the expression:
a. 10 log 4
b. log5 25x
Find the inverse of the function:
a. y 6 x
b. y ln x 3
Simplify the expression:
log8 x
27. 8
28. log7 7
3x
Algebra 2
29. log2 64 x
30. eln 20
31. Find the inverse of y 4 x .
32. Find the inverse of y ln x 5 .
Your assignment is: Pages 503 – 504: 3-43 odd.