8­3 Day 1 Logarithmic Functions as Inverses 2010
April 09, 2010
8­3 Day1 Logarithmic Functions as Inverses
1 yaD 3­8
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Objectives: Convert between exponential form and logarithmic form.
Apply logarithms to real world situations.
Mar 18­10:32 AM
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8­3 Day 1 Logarithmic Functions as Inverses 2010
April 09, 2010
Check Skills You'll Need
Find the inverse of each function.
1) y = 3x ­ 2
2) y = ¾x + 5
3) y = x2 + 7
4) y = 2x2 ­ 9
Mar 18­11:00 AM
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8­3 Day 1 Logarithmic Functions as Inverses 2010
April 09, 2010
Find the value of x in each example.
1) 3x = 27
2) 5x = 625
3) 4x = 1024
4) 2x = 2048
We need an easier way to solve these problems, but how do you undo exponents?
Mar 18­11:06 AM
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8­3 Day 1 Logarithmic Functions as Inverses 2010
April 09, 2010
Recall that :
Inverse functions are two functions whose operations undo each other.
Find the inverse of an exponential function.
bx= y
switch the variables and solve for y
by= x
We run into the same problem, how do we solve for y?
We need an inverse function for exponents.
This function is called a logarithm.
Mar 18­10:50 AM
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8­3 Day 1 Logarithmic Functions as Inverses 2010
April 09, 2010
Logarithms are defined in the following way:
If bx= y, then logb y = x
pronounced "log base b of y equals x"
Using the definition rewrite the following exponential functions in logarithmic form.
25 = 32
32 = 9
43 = 64
Mar 18­11:03 AM
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8­3 Day 1 Logarithmic Functions as Inverses 2010
April 09, 2010
Using the definition, rewrite these logarithmic functions in exponential form.
log5 625 = 4
log10 10000 = 4
loge 54.598 ≈ 4
Mar 18­11:04 AM
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8­3 Day 1 Logarithmic Functions as Inverses 2010
April 09, 2010
Evaluating Logarithmic Functions
Mar 18­11:18 AM
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8­3 Day 1 Logarithmic Functions as Inverses 2010
April 09, 2010
Evaluate each logarithm.
a. log64 (1/32) b. log9 27
c. log10 100
Mar 18­11:19 AM
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8­3 Day 1 Logarithmic Functions as Inverses 2010
April 09, 2010
A COMMON LOGARITHM is a logarithm that uses base 10. You can write the common logarithm
log10 y as log y.
The log button on your calculator is used for base 10 calculations.
Mar 18­11:20 AM
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8­3 Day 1 Logarithmic Functions as Inverses 2010
April 09, 2010
Use your calculator to evaluate each logarithm to four decimal places.
a. log 9
b. log (3/7)
c. log (­10)
WHY does the third problem fail? Rewrite it in exponential form to make it easier to see.
Mar 20­2:43 PM
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8­3 Day 1 Logarithmic Functions as Inverses 2010
April 09, 2010
homework
page 449
#6­25, 41, 43­46, 48, 53 ­ 61
Mar 18­11:22 AM
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