Solving Logarithmic Equations Worksheet With Answer Key Page 3
ADVERTISEMENT
1
2
3
4Example 5
Solve each equation.
1
1
b. log
-(5x - 3) = log
-(10x + 2)
a. log
6561 =
4
5
5
p
2
1
log
-(5x - 3) = log
-(10x + 2)
1
5
5
log
6561 =
4
p
2
-(5x - 3) = -(10x + 2)
5x = -5
1
1
=
p
2
6561
4
x = -1
4
p =
6561
2
2
( p)
= (9)
p = 81
c. log
(x + 1) + log
(x + 3) = log
24
8
8
8
log
(x + 1) + log
(x + 3) = log
24
8
8
8
log
[(x + 1)(x + 3)] = log
24
8
8
2
x
+ 4x + 3 = 24
2
x
+ 4x - 21 = 0
(x + 7)(x - 3) = 0
x + 7 = 0
or
x - 3 = 0
x = -7
x = 3
=
By substituting x = -7 and x
3 into the equation, we find that x = -7 is undefined for the equation
log
(x + 1) + log
(x + 3) = log
24. When x = -7 we get an extraneous solution.
8
8
8
So, x = 3 is the correct solution.
Example 6
Graph y = log
(x + 2).
4
y
The equation y = log
(x + 2) can be written as 4
= x + 2. Choose values for y and then find the
4
corresponding values of x.
x + 2
(x, y)
y
x
-3
0.016
-1.984
(-1.984, -3)
-2
0.063
-1.937
(-1.937, -2)
-1
0.25
-1.75
(-1.75, -1)
0
1
-1
(-1, 0)
1
4
2
(2, 1)
2
16
14
(14, 2)
3
64
62
(62, 3)
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education