1. Logarithmic Functions as Inverses.
What you’ll learn
To write and evaluate logarithmic expressions.
To graph logarithmic functions.
To solve problems involving functions and their
inverses.
Vocabulary
Logarithm, logarithmic function,
common logarithm, logarithmic scale

2. Take a note:
The exponential function is one to one,
so its inverse is a function. To express
“y as a function of x” for the inverse, write
Logarithm: A logarithm base b of a positive
number x satisfies the following definition.
For
You can read “as log base b of x”.
In other words, the logarithm y is the exponent to
which b must be raised to get x.

3. Problem 1: Writing Exponential Equations in Logarithmic Form
What is the logarithmic form of each equation?
Your turn

4. Problem 2: Evaluating a Logarithm.
What is the value of
Write a logarithm equation
Use the definition of a log
to write an exponential equation
Write each side using base 2
Power property of the exponents
Since the base is the same the
exponents must be equal

5. Your turn
What is the value of each logarithm?
Answers
Take a note: A common logarithm is a logarithm with
base 10. You can write a logarithm
When you use the logarithm of a quantity instead
of the quantity, you are using Logarithm Scale.

6. Problem 3: Using a Logarithmic
In December 2004, an earthquake with magnitude 9.3 on the Richter scale hit off the northwest coast of Sumatra. The diagram shows the magnitude of an earthquake that hit Sumatra in March’05 was8.7. The formula compares the intensity levels of earthquakes where I is the intensity level determined by a seismograph, and M is the magnitude on a Richter scale. How many times more the intense was the December earthquake that the March earthquake?

7. Your turn Answer: Answer:
In 1995, an earthquake in Mexico registered
8.0 on the Richter scale. In an earthquake of
magnitude 6.8 shock Washington state. How many
times more intense was 1995 earthquake than
2001 earthquake?
Answer:
b) The loudness of a sound in decibels, dB, is defined
as , where I is the intensity of the sound.
How loud is a whisper with an intensity of ?
Answer:

8. Remember that the graphs of inverse function are
A logarithmic function is the inverse of an exponential function. The graph shows and its inverse
Exponential function
Remember that the graphs of
inverse function are
reflections of each other
across the line y=x.
Logarithmic function

10. How does the graph of compare to the graph of the parent function? x y
Your turn
How does the graph of compare
to the graph of the parent function?
Step 2: Graph the parent function then shift the graph to the right3 units and up 4 units to the graph
Step 1: Make the table x y -2 -1 1 4 16 2

11. Classwork odd Homework even
TB pgs exercises 12-79