Download 6.6: Log and Exp. Equations

Section 6.6
Logarithmic and
Exponential Equations
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Recall:
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Solve: log3 4  2log3 x
log 3 4  log 3 x 2
4  x2
x  2 or x  2
Reminder: The domain of logarithmic functions is positive
numbers only so check for extraneous solutions.
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Solve: log2  x  2  log2 1  x   1
log2  x  21  x   1
2   x  21  x 
2   x2  x  2
x2  x  0
x  x  1  0
x  0 or x  1
Both solutions are in the
domain of the log functions.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Recall:
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Solve: 3  7
x
ln 3x  ln 7
x ln 3  ln 7
ln 7
x
 1.771
ln 3
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Solve: 5  2 x  3
3
x
2 
5
3
ln 2  ln  
5
x
3
x ln 2  ln  
5
3
ln  
5

x
 0.737
ln 2
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Solve: 2 x 1  52 x 3
ln 2 x 1  ln 52 x 3
 x 1 ln 2   2x  3 ln 5
x ln 2  ln 2  2x ln5  3ln5
x ln 2  2x ln5  3ln5  ln 2
x  ln 2  2ln 5  3ln 5  ln 2
3ln 5  ln 2
x
 2.186
ln 2  2 ln 5
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Solve: 9 x  3x  6  0
x
 
Note that 9 = 3
x
2
so the equation is quadratic in form.
u2  u  6  0
u  3x and u 2 = 9 x
u  3u  2  0
u  3 or u  2
3  3 or 3  2
x
x
3x  0 for all x
x 1
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.