Download Lesson 6 - Coweta County Schools

Notes Over 8.6
Solving by Equating Exponents
Solve the equation.
3x
x 8
1. 5  5
3x  x  8
2x  8
x4
2 x 3
4 x 1
2. 10
 10
2x  3  4x 1
4  2x
x2
Notes Over 8.6
Solving by Equating Exponents
Solve the equation.
2 x  1/ 2 
3. 25 2 x1/ 2   125
3 x
2
5   5 
3x
4 x 1
5
5
4 x  1  3x
1  x
x  1
x
Notes Over 8.6
Solving by Equating Exponents
Solve the equation.
x 1
4. 16  4
x 1
2
4 4
2  x 1
x 1
Notes Over 8.6
Taking a Logarithm of Each Side
Solve the equation.
x
5. 5  8
x
log 5  log 8
x log 5  log 8
log 5 log 5
x  1.292
x
6. e  5
x
ln e  ln 5
 x  ln 5
x  1.609
Notes Over 8.6
Taking a Logarithm of Each Side
Solve the equation.
x
7. 2  1  5
8. 10  6  146
2x
x
10  152
2 4
x
2x
log 2  log 4
log 10  log 152
2 x  log 152
x log 2  log 4
2
2
log 2 log 2
x  1.091
x2
2x
Notes Over 8.6
Taking a Logarithm of Each Side
Solve the equation.
9. 9  4e  5
x
 4e  4
x
e 1
x0
x
1 2 x
10. e  6
2
2 x
 12
2 x
ln e  ln 12
 2 x  ln 12
2 2
x  1.242
e
Notes Over 8.6
Solving a Logarithmic Equation
Solve the equation.
11. log x  3  log 3x  1
x  3  3x  1
3  2x 1
2  2x
x 1
Notes Over 8.6
Solving a Logarithmic Equation
Solve the equation.
12. log 2 x 1  log 2 2 x  1
x 1  2x  1
1  x  1
x  2
Notes Over 8.6
Solving a Logarithmic Equation
Solve the equation.
13. ln 4  x  ln 4 x 11
4  x  4 x 11
4  5x 11
15  5x
x3
Notes Over 8.6
Exponentiating Each Side
Solve the equation.
2
14. log 8 x  5 
3
8
log8  x 5 
8
x 5  4
x9
2/3
Notes Over 8.6
Exponentiating Each Side
Solve the equation.
15. 3 log 5 x  2  6
log 5 x  2  2
5
log5  x  2 
5
2
x  2  25
x  23
Notes Over 8.6
Exponentiating Each Side
Solve the equation.
16. 4 ln 2 x  5
5
ln 2 x 
4
e
ln 2 x
e
5/ 4
2 x  3.49
x  1.74
Notes Over 8.6