Alg2 4.4 Notes.notebook
November 09, 2012
4­4 Properties of Logarithms
Skills we've learned
Quiz after this lesson, so let's get started
Warm­up Answers
Alg2 4.4 Notes.notebook
November 09, 2012
4­4 Properties of Logarithms
Use properties to simplify logarithmic expressions
Translate between logarithms in any base
Seismologists, to calculate energy released by earthquakes
I. Product Property of Logarithms
Express as a single logarithm. Simplify.
1) log64 + log69 Alg2 4.4 Notes.notebook
November 09, 2012
Think: logj + loga + logm = logjam
Express as a single logarithm. Simplify.
2) log5625 + log525
3)
II. Quotient Property of Logarithms
Express as a single logarithm. Simplify, if possible.
4) log5100 – log54 Alg2 4.4 Notes.notebook
November 09, 2012
Express as a single logarithm. Simplify, if possible.
5) log749 – log77 III. Power Property of Logarithms
Express as a product. Simplify, if possible.
6) log2326
Alg2 4.4 Notes.notebook
November 09, 2012
Express as a product. Simplify, if possible.
7) log8420
8) log104
9) log5252
10)
IV. Inverse Property of Logarithms
11) log3311
12) 13) log381
Alg2 4.4 Notes.notebook
November 09, 2012
14) Simplify log100.9
15) Simplify
V. Change of Base
16) Evaluate log328
How many ways can we do this?
Alg2 4.4 Notes.notebook
November 09, 2012
17) Evaluate log527
18) Evaluate log816
VI. All Together
19)
20)
Alg2 4.4 Notes.notebook
November 09, 2012
VII. Application
21) The tsunami that devastated parts of Asia in December 2004 was spawned by an earthquake with magnitude 9.3 How many times as much energy did this earthquake release compared to the 6.9­magnitude earthquake that struck San Francisco in1989?
Alg2 4.4 Notes.notebook
November 09, 2012
How would we expand ? 4­4 p.260 #3 ­ 11 odd, 12, 15 ­ 19 odd, 25, 26, 29, 30, 32, 34, 36 ­ 41, 43, 51, 57 ­ 68, 70 ­ 75, 78 ­ 80
*44 problems!