warm-up: simplify each of the following. homework solutions
TRANSCRIPT
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Warm-Up: Simplify each of the following
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24.0
25.-3
26.3
27.-2
28.Ask for graphs
29.Ask for graphs
Homework Solutions
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• Do you guys remember the natural base?– e
• Well just like there is a natural base, there is a natural log as well.– that is the natural log and the notation for that is ln– The natural log and natural base are inverses of each other
Natural Logarithm
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• How to find using our calculator.– In TI-84, hit ALPHA, WINDOW and there is an option to insert a log
with a base other than 10.– For TI-83, use the change of base formula in your calculator
– When given – You can also do
• Now find
Calculator Exploration
Both yields the same answer
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Properties of Logarithms
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• Work in pairs to complete the handout.
• It is ok if you don’t finish it all when we go over it, just work on what you can.
Properties of Logarithms Exploration
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1b).
2b).
1a).
2a).
Product Property
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General Rule
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1b).
2b).
1a).
2a).
Quotient Property
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General Rule
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1b).
2b).
1a).
2a).
Power Property
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General Rule
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• Remember how I told you yesterday that logarithms are the inverse of exponentials.
• Also remember I told you another way to read logarithms is “the log is the exponent”
• Well I want you to notice something:– When you have you add the exponents.– When you have you subtract the exponent.– When you have you multiply the exponents.
Remember…
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log 4 𝑥5Example 1: Expand the expression
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ln3 𝑦 4
𝑥3
Example 2: Expand the expression
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Worksheet #26
Homework