PreCalculus: Lesson Plan * 10/25/2006

Quickstart
Writing About Math p.235
Human Memory Model

Lesson
3.3 Properties of Logarithms (continued)
Objective: Students will know how to rewrite logarithmic functions with a different base, use properties of logarithms to evaluate, rewrite, expand, and condense logarithmic expressions.

III. Rewriting Logarithms (continued)
Example 3
Condense the logarithmic expression
a) 2log - 3logy + 1/2·logz
= log x² - log y³ + log√z
= log (x²/y³) + log√z
= log (x²√z/y³)
b) 1/3(2lnx - 4 ln y - ln(z + 2)
= 1/3(lnx² - ln y⁴ - ln(z+2))
= 1/3[ln(x²/[y⁴(z + 2)])]
= ln ³√x²/[y⁴(z + 2)]

IV Application
Example 4: On the Richter Scale, the magnitude R of an earthquake of intensity I is given by
R = (lnI - lnI₀)/ln 10, where I₀ is the minimum intensity used for comparison. Write this as a single common logarithmic expression.
R = (lnI - lnI₀)/ln 10
= (log I/log e) - (log I₀ / log e)
——————————————————— Using Change of Base formula
(log 10/log e)
= log I - log I₀
——————— Multiply by log e / log e
log 10
= log I - log I₀ log 10 = 1
= log (I / I₀) Quotient property

Read about and watch a video news report about the magnitude 6.0 earthquake that struck in the Gulf of Mexico September 10th, 2006.

This map shows where people have reported to the United States Geological Survey (USGS) that they felt the earthquake.

Homework
p.244 - 246 #3 - 67 odd