chapter 4 4-5 exponential and logarithmic equations
TRANSCRIPT
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Chapter 4 4-5 Exponential and logarithmic
equations
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Objectives
Solve exponential and logarithmic equations and inequalities.
Solve problems involving exponential and logarithmic equations.
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Exponential equationO An exponential equation is an
equation containing one or more expressions that have a variable as an exponent.
O To solve exponential equations:•Try writing them so that the bases are all the same.
•Take the logarithm of both sides.
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Example#1O Solve for xO 98 – x = 27x – 3
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Example#2O Solve for x
O 4x – 1 = 5
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Example#3O Solve O 23x = 15
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Student guided practice
O Do problems 2 -5 in your book page 270
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Biology Application O Suppose a bacteria culture
doubles in size every hour. How many hours will it take for the number of bacteria to exceed 1,000,000?
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Logarithmic equationO A logarithmic equation is an
equation with a logarithmic expression that contains a variable. You can solve logarithmic equations by using the properties of logarithms.
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Example#4O Solve
O log6(2x – 1) = –1
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Example#5O Solve
O log4100 – log4(x + 1) = 1
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Example#6O Solve
O log5x 4 = 8
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Student guided practice
O Do problems 9 -13 in your book page 270
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Example#7O Use a table and graph to solve O 2x + 1 > 8192x.
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Example#8O Using a table and graph solve
O log(x + 70) = 2log( x/3 )
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Example#9
Use a table and graph to solve 2x > 4x – 1.
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Student guided practice
O Do problems 17-19 in your book page 270
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Homework O Do even problems from 21-36 in
your book page 270
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Closure
Today we saw how to solve exponential and logarithmic functions.Next class we are going to continue with the natural base , e.