44 Properties of Logarithms - bisd303.org
Transcript of 44 Properties of Logarithms - bisd303.org
Alg2 4.4 Notes.notebook November 09, 2012
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44 Properties of Logarithms
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Alg2 4.4 Notes.notebook November 09, 2012
44 Properties of Logarithms
Use properties to simplify logarithmic expressionsTranslate between logarithms in any base
Seismologists, to calculate energy released by earthquakes
I. Product Property of Logarithms
1) log64 + log69 Express as a single logarithm. Simplify.
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
4) log5100 – log54
Express as a single logarithm. Simplify, if possible.
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
12) 13) log38111) log3311
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. Application21) 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!