8­6 Day 2 Natural Logarithms
April 13, 2009
8­6 Day 2 Natural Logarithms
Objective:
Solve equations using natural logarithms.
Apr 10­5:01 PM
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8­6 Day 2 Natural Logarithms
April 13, 2009
Check Skills You'll Need
Use the properties of logarithms to evaluate each expression.
1. log2 8 ­ log2 4
2. ¾ log 10 + 7 log 100
3. 7 log8 49
Apr 10­5:08 PM
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8­6 Day 2 Natural Logarithms
April 13, 2009
Solving a Natural Logarithmic Equation
Solve ln (3x + 5)2 = 4.
Check your answers:
ln (3x + 5)2 = 4
(3x + 5)2 = e4
(3x + 5)2 = 54.6
3x + 5 = ±√54.6
3x + 5 = 7.39 or ­7.39
x = 0.797 or x = ­4.13
Apr 10­5:14 PM
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8­6 Day 2 Natural Logarithms
April 13, 2009
You try! Solve the following problems.
( x + 2
3 (
a. ln x = 0.1
b. ln = 12
Apr 10­5:29 PM
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8­6 Day 2 Natural Logarithms
April 13, 2009
Solving an Exponential Equation
Solve 7e2x + 2.5 = 20.
7e2x + 2.5 = 20
7e2x = 17.5
e2x = 2.5
ln e2x = ln 2.5
2x ln e = ln 2.5
2x = ln 2.5
x = (ln 2.5)/2
x ≈ 0.458
SLIDE
Apr 10­5:28 PM
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8­6 Day 2 Natural Logarithms
April 13, 2009
You would like to go to the Master's Tournament. Right now you have $1500. If you invest this money in an account that compounds continuously at a rate of 6.5%, how many years will it take for you to have $4000 in your account so you have enough money to go to the tournament?
Apr 10­5:46 PM
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8­6 Day 2 Natural Logarithms
April 13, 2009
HOMEWORK
Chapter 8 Review
Apr 10­5:57 PM
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