3/30/2015
7-4 Properties of Logarithms
The Plan For Today
• Questions on 7-3
• Daily L to J
• Lesson 7-4 (p.512-515)
1. Cards
2. Groups – You Pick
3. Groups - #
4. Volunteers – 1 +
5. Combo
6. Students’ Choice
7-4 Properties of Logarithms
Remember that to multiply
powers with the same base,
you add exponents.
Use properties to simplify
logarithmic expressions.
Translate between logarithms in
any base.
• Assignment 7-4
Quiz: 7-1 to 7-4 – Tues. 3/31
HWQ #10 – Wed. 4/1
Holt Algebra 2
Holt Algebra 2
7-4 Properties of Logarithms
7-4 Properties of Logarithms
Example 1: Adding Logarithms
Express log64 + log69 as a single logarithm.
Simplify.
Remember that to divide
powers with the same base,
you subtract exponents
Because logarithms are exponents, subtracting
logarithms with the same base is the same as
finding the logarithms of the quotient with that
base.
Holt Algebra 2
7-4 Properties of Logarithms
Holt Algebra 2
7-4 Properties of Logarithms
Example 2: Subtracting Logarithms
Express log5100 – log54 as a single logarithm.
Simplify, if possible.
The property above can also be used in reverse.
Caution
Just as a5b3 cannot be simplified, logarithms
must have the same base to be simplified.
Holt Algebra 2
Holt Algebra 2
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3/30/2015
7-4 Properties of Logarithms
7-4 Properties of Logarithms
Example 3: Simplifying Logarithms with Exponents
Because you can multiply logarithms, you can
also take powers of logarithms.
Express as a product. Simplify, if possible.
A. log2326
Holt Algebra 2
Holt Algebra 2
7-4 Properties of Logarithms
7-4 Properties of Logarithms
Check It Out! Example 3
Exponential and logarithmic operations undo each
other since they are inverse operations.
Express as a product. Simplify, if possibly.
a. log104
Holt Algebra 2
Holt Algebra 2
7-4 Properties of Logarithms
7-4 Properties of Logarithms
Example 4: Recognizing Inverses
Most calculators calculate logarithms only in base
10 or base e (see Lesson 7-6). You can change a
logarithm in one base to a logarithm in another
base with the following formula.
Simplify each expression.
a. log3311
Holt Algebra 2
b. log381
c. 5log 10
5
Holt Algebra 2
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3/30/2015
7-4 Properties of Logarithms
Example 5: Changing the Base of a Logarithm
Evaluate log328.
7-4 Properties of Logarithms
Logarithmic scales are useful for measuring
quantities that have a very wide range of
values, such as the intensity (loudness) of a
sound or the energy released by an
earthquake.
Helpful Hint
The Richter scale is logarithmic, so an increase of
1 corresponds to a release of 10 times as much
energy.
Holt Algebra 2
Holt Algebra 2
7-4 Properties of Logarithms
7-4 Properties of Logarithms
Today’s Assignment
7-4
p. 516-519
21-33 odd, 37-45 odd,
48-49, 66-68,
82-96 even
Holt Algebra 2
What did you like?
What didn’t you like?
What did you learn?
What isn’t quite clear?
______ is awesome!
Please stop _________.
Anything else…
Holt Algebra 2
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