lesson+7.3

Aim: 1. What is a logarithm? 2. How do we convert from exponential form to logarithmic form? 3. How can solve for simple logarithms? 4. What is the relationship between graphs of exponents ad graphs of logarithms? 5. How can we graph a logarithm using phase shifts (transformations)? 6. How can logarithms be used to solve problems?

Here is a short video on how to convert from exponents to logarithms. How are logarithms related to exponents?

media type="youtube" key="mQTWzLpCcW0" width="425" height="350"

Now try some yourself: 1. Change each to logarithmic form: a. 100=10^2 b. 81 = 3^4 c. 1 = 3^0

2. Find the value of each... a. log(5) 125 b. log(4) 32 c. log(64) 1/32 d. log1000=3 (When a base is not given, it is base =10)

Here is a short video how to graph a logarithmic function. Notice the logathimic function is the inverse of an exponential function. This video also shows a transformation of a logarithmic function. All inverses have a line of symmetry. What is the equation for the line of symmetry? media type="youtube" key="d7g0GrQwJsY" width="425" height="350"

Now graph some of your ownin your notebook. Be sure to use the transformation tricks from the last lesson 1. y=log(3) x 2. y=log(4) log(x - 3) + 4 3. y=log(2) log(x + 1) - 2 4. y=5log(2)x

The Richter Scale measures the strength of earth quakes. Try this problem based on earthquakes. In December 2004, an earthquake with magnitude 9.3 on the Richter scale hit off the northwest coast of Sumatra. Another earthquake hit near the same spot in March 2005. its magnitude on the Richter scale was 8.7. The formula log//(//I1/I2) //=// M(1) - M(2) compares the intensity levels of earthquakes where I is the intensity level determine by a seismograph, and M is the magnitude on a Richter scale. How many times more intense was the December earth than the March earthquake? Use your graphing caluclator. (Ans: About 4)