*Section 8.3 Logarithmic Functions as inverse Day 1
Tuesday, January 29, 2013
6:16 PM
How many 2's do you need to multiply together in order to equal 8?
So it takes 3 twos to equal 8. The 3 is called a logarithm.
The way that logarithm is written is as follows.
Logarithm
The logarithm to the base b of a positive number y is defined as follows:
A logarithm is the power to which a number must be raised in order to get some other number.
Ex. 1 Write the equation in logarithmic form. a) b) c)
Chapter 8 Page 1

To evaluate logarithms, you can write them in exponential form then simplify.
Ex. 2 a) b) c)
The common logarithm is a logarithm that uses base 10.
The common log can be written as:
So, if you see a log with out a base that means it is base
10.
Ex. 3 a) b)
Chapter 8 Page 2

Scientist use common logs to measure acidity which increases as the concentration of hydrogen ions in a substance increases. The pH of a substance equals:
Ex. 4
Find the concentration of hydrogen ions in the following fruit. Then, compare to see which fruit is more acidic.
a) Apple with pH 3.3 b) Banana with pH 5.2
The Richter scale
The Richter scale is used to measure the amount of energy released in an earthquake. Each number on the scale is an increase of energy by 30 times.
Chapter 8 Page 3

The exponents on this scale is a logarithm
Ex. 5
April 18, 1906 San Francisco experienced an earthquake that measured 7.8 on the Richter scale. Then, on
October 17, 1989 the bay area experienced another earthquake that measured 6.9. Compare each of them to the earthquake in Japan on March 11, 2011 measuring
9.0.
Chapter 8 Page 4