Transcript Lesson 4 - Log Equations using Log Properties

More on Log
Equations
Solve:
log100  x
10  100
x
10  10
x2
x
2
Solve:
 1 
log 3    x
 27 
1
3 
27
x
3
3 3
x  3
x
Solve:
1
log 64 x 
3
1
3
64  x
x  64
x4
3
log3 7
3
Solve:
Base
x
Exponent
HINT :
If log b x  log b y, then x  y.
log 3 x  log 3 7
x7
Solve:
log5 12
5
x
log 5 x  log 5 12
x  12
log x 3  8
4
Solve:
x
8
3
x 
1

8 8

1
2
x3
1
x 1
x
32
1
3
4
 
 3
1

4 8
Solve:
log 4 (5 x  1)  log 4 8
HINT :
If log b x  log b y, then x  y.
5x  1  8
5x  9
9
x
5
Solve:
log3  2 x  1  4
3  2x  1
4
81  2 x  1
2 x  82
x  41
Solve:
log 3 x  log 3 ( x  2)  3
log 3 x x  2  3
Solve with Quadratic Formula :
33   x x  2 
x 2  2 x  27  0
NOTE : We cannot use
the MINUS solution because the domain
of a log function is all
POSITIVE real numbers.
 b  b 2  4ac 2  4  41 27 
x

2a
21
2  4  108 2  16 7


2
2
24 7

 1 2 7
2
Solve:
log 2  7 x  2   5
2  7x  2
5
32  7 x  2
7 x  34
34
x
7
Solve:
log (3x  2)  log ( x  2)  log (7 x  6)
log 3x  2x  2   log 7 x  6
3x  2x  2  7 x  6
3x 2  8 x  4  7 x  6
3x 2  x  2  0
3x  2x  1  0
2
x  , x  1
3
NOTE : We cannot use
x  1 because the domain
of a log function is all
POSITIVE real numbers.
Solve:
log 4 x  log 4  x  6   2
log 4  x  x  6   2
4 2   x  x  6 
16  x  6 x
2
x  6 x  16  0
x  8x  2  0
2
x  8, x  2
Solve:
log3  x  2   log 3 x  2
x2
log 3
2
x
x2
2
3 
x
x2
9
x
9x  x  2
8x  2
1
x
4
Solve:
log 2 (3x  1)  log 2 2  log 2 4  log 2 ( x  3)
log 2 3x  12  log 2 4x  3
6 x  2  4 x  12
2 x  14
x7