8­6 Day 1 Natural Logarithms
April 10, 2009
8­6 Day 1 Natural Logarithms
Objective: Evaluate natural logarithmic expressions.
Mar 21­6:47 PM
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8­6 Day 1 Natural Logarithms
April 10, 2009
Check Skills You'll Need
Use your calculator to evaluate each expression to the nearest thousandth.
1. e5
2. 2e3
3. e­2
4. 1/e
5. 4.2e
Solve:
6. log3 x = 4
7. log16 4 = x
8. log16 x = 4
Mar 21­7:00 PM
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8­6 Day 1 Natural Logarithms
April 10, 2009
In lesson 8­2 you learned that e ≈ 2.71828.
A logarithm that has a base of e has a special name called a NATURAL LOGARITHM.
Instead of writing loge x, we now write natural logarithms like this: ln x.
Therefore,
loge x = ln x
Mar 21­7:06 PM
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8­6 Day 1 Natural Logarithms
April 10, 2009
INVERSES
The properties of common logarithms apply to natural logarithms as well.
Mar 21­7:17 PM
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8­6 Day 1 Natural Logarithms
April 10, 2009
Simplifying Natural Logarithms
Write 3 ln 6 ­ ln 8 as a single natural logarithm.
Mar 21­7:29 PM
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8­6 Day 1 Natural Logarithms
April 10, 2009
Try some more!
b. 3 ln x + ln y
c. ¼ ln 3 + ¼ ln x
Mar 21­7:30 PM
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8­6 Day 1 Natural Logarithms
April 10, 2009
With a partner, answer this question:
What is ln e?
loge e = x
ex = e
x must be 1
Therefore, ln e = 1
Mar 21­7:53 PM
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8­6 Day 1 Natural Logarithms
April 10, 2009
There is a special button on your calculator for natural logarithms. Use that button to evaluate the following to four decimal places:
a. ln 4 b. 7 ln 3.2
c. ½ ln 2 ­ 2 ln 5
d. ln (­6)
Why can't you take the natural log of a negative number?
Mar 21­8:06 PM
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HOMEWORK
8­6 Day 1 Natural Logarithms
April 10, 2009
p. 472 #1­11, 31­38
Extra Credit: #41­43 (Show Work)
Mar 21­7:30 PM
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