Embed Size (px)
Citation preview
Main Ideas/Questions Notes/Examples
Solving
(using a common base)
Steps to solve an exponential equation using a common base:
1 Rewrite the equation using a common base.
2 Use the properties of exponents to simplify each side of the equation.
3 Use the one-to-one property: If ,x yb b then
4 Solve!
WITH A COMMON BASE
(
1. 2 9 73 3x� 2. 4 1 5 2w we e� �
3. 1 3 2 7 165 5 5c c c� � �� 4. 2 2 9 4 118 8 8 8k k k k� �� �
WITHOUT A COMMON BASE
5. 4 269 81y � 6. 2 41 4
64a �
7. 9 32 32m m� � 8.
24 3
2 131 12 1212
xx x
�
�§ · � ¨ ¸© ¹
Name: ___________________________________________________________________
Class: ___________________________________________________________________
Date:
Topic: ___________________________________________________________________
x y
© Gina Wilson (All Things Algebra®, LLC), 2017
9. 4
2 4 134349
nn
�
� § · ¨ ¸© ¹
10. 2 38 128v v� �
11. 2 69 243p p� � 12.
2 22 6 2 51 14 64
x x� �§ · § · ¨ ¸ ¨ ¸© ¹ © ¹
13. 2 136 21636
r � 14. 3 125 62525
a a��
15. 7 4
51 16416 32
xx
�
�§ · § ·� ¨ ¸ ¨ ¸© ¹ © ¹
16. 2
23 51 1512
64 8
y yy § · § · �¨ ¸ ¨ ¸
© ¹ © ¹
© Gina Wilson (All Things Algebra®, LLC), 2017
Name: _______________________________ Unit 4: Exponential & Logarithmic Functions
Date: _____________________ Per: _______
Homework 7: Solving Exponential Equations (using a common base)
Directions: Solve each equation using a common base. 1. 3 8 137 7y� 2. 5 6 1210 10x x� �
3. 7 2 1 8 363 3 3p p p� � �� 4. 2 9 2 5 3 4k k k ke e e e� � � �� �
5. 3 7 114 16w� 6. 9 2 38 32x x� �
7. 2
28
31 1255
uu
�
�§ · ¨ ¸© ¹
8. 4
4 91 3 327
cm
�
�§ · �¨ ¸© ¹
** This is a 2-page document! **
© Gina Wilson (All Things Algebra®, LLC), 2017
9. 4 2 39 243a a� � 10. 1 316 64m m� �
11. 2 21 1
216 36
k k� �§ · § · ¨ ¸ ¨ ¸© ¹ © ¹
12.
2 22 3 549 343x x� �
13. 2 3
3 1 1168 32
yy
�
� § ·� ¨ ¸© ¹
14. 7 2 3 225 625 1p p� ��
15. 2 1
21 27 8181
w§ · � ¨ ¸© ¹
16.
2 2 24 16 64a a a� �
© Gina Wilson (All Things Algebra®, LLC), 2017
Main Ideas/Questions Notes/Examples
Solving
Type 1:
log = log
1 Condense the logarithms on each side of the equation.
2
Use the one-to-one property: If log log ,b bx y then
3 Solve and check for extraneous solutions.
Directions: Solve each equation. Check for extraneous solutions. 1. 3 37 1 5 17log ( ) log ( )x x� � 2. 2 4 14ln ( ) ln ( )k k k� �
3. 64 3 8log log ( ) logc� � 4. 7 7 7
16 5 3 83
log ( ) log ( ) logw w� � � �
5. 44 4
14 3 162
log ( ) log ( )p p� �
6. 32 1 80 52
ln( ) (ln ln )a� � �
Name: ___________________________________________________________________
Class: ___________________________________________________________________
Date:
Topic: ___________________________________________________________________
x y
© Gina Wilson (All Things Algebra®, LLC), 2017
Solving
Type 2:
log = number
1 Condense and isolate the logarithm.
2 Rewrite the equation in exponential form.
3 Solve and check for extraneous solutions.
Directions: Solve each equation. Check for extraneous solutions. 7. 2 3 4 7log ( )x � 8. 2 9ln a
9. 6 7 5 3log ( )w � � � 10. 292 2 4 5log ( )k k� � �
11. 4 42 3 2 3 2log ( ) log ( )v v� � �
12. 1 27 5 43ln ln( )x� � �
13. 2 23 1 5log ( ) log ( )n n� � � 14. 22 2 3 5 2log log ( )c c� �
© Gina Wilson (All Things Algebra®, LLC), 2017
Name: _______________________________ Unit 4: Exponential & Logarithmic Functions
Date: _____________________ Per: _______
Homework 8: Solving Logarithmic Equations
Directions: Solve each equation. Check for extraneous solutions. 1. 7 76 4 9 5log ( ) log ( )a a� � 2. 6 6 63 11 2 4 8log ( ) log log ( )x x� � �
3. 3 2 1 4ln( ) ln( ) lnm m� � � 4. 2 24 42 3 10log ( ) log ( )p p p� �
5. 81 16 3 124ln( ) ln lnq� �
6. 6 2 3 4log log( ) logy� � �
7. 5 5 533 12 405 54
log ( ) (log log )k � � � 8. 8 8 812 3 4log ( ) log ( ) logw w� � �
** This is a 2-page document! **
© Gina Wilson (All Things Algebra®, LLC), 2017
9. 6 11 18 3log ( )p � 10. 22 3 7 10log ( )x� �
11. 4 3 5ln( )u � 12. 27
1 25 62 3log ( )c� �
13. 2 2 1 0log( )a� � 14. 12 43
ln ln( )k� �
15. 22 22 3 3log ( ) log ( )w w� � 16. 2
12 12114 4 22
log ( ) log ( )n n� � �
© Gina Wilson (All Things Algebra®, LLC), 2017
Main Ideas/Questions Notes/Examples
Solving
(using logarithms)
If using a common base is not possible, exponential equations can be solved using logarithms.
1 Isolate the exponential expression.
2 Take the logarithm of each side.
3 Expand the logarithms if necessary using the power rule.
4 Solve and check for extraneous solutions.
(
1. 3 80x 2. 140xe
3. 15 18x� 4.
2 51 1203
x�§ · ¨ ¸© ¹
5. 3 25 108xe � 6. 42 8 50x�� � �
Name: ___________________________________________________________________
Class: ___________________________________________________________________
Date:
Topic: ___________________________________________________________________
x y
© Gina Wilson (All Things Algebra®, LLC), 2017
7. 62 2 1 413
x�� � 8. 2 72 4 9 55x�� � � �
9. 5 22 3x x� � 10. 2 1 38 5x x� �
11. 3 3 24 11x x� � 12. 2 5 49 2x x� �
© Gina Wilson (All Things Algebra®, LLC), 2017
Name: _______________________________ Unit 4: Exponential & Logarithmic Functions
Date: _____________________ Per: _______
Homework 9: Solving Exponential Equations (using logarithms)
Directions: Solve each exponential equation using logarithms. 1. 7 15q 2. 222 9x
3. 82 7
3 4
r�§ · ¨ ¸© ¹
4.
64
me
�
5. 2 95 6 14k�� 6. 413 9 4a � �
7. 6 52 147
ye ��
8. 1 48 11 9 41p�� �
** This is a 2-page document! **
© Gina Wilson (All Things Algebra®, LLC), 2017
9. 2 56 7 10 78
n�� � � 10. 34 7 35
9ye�� �
11. 2 25 8c c� 12. 4 1 36 2k k� �
13. 1 3 52 7p p� � 14. 2 4 4 14 10m m� �
© Gina Wilson (All Things Algebra®, LLC), 2017
