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

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.

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

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

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.

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?

Your turn Answer: Answer: In 1995, an earthquake in Mexico registered 8.0 on the Richter scale. In 2001 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:

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

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

Classwork odd Homework even TB pgs. 456-457 exercises 12-79