LAWS OF LOGARITHMS
SECTION 5.6
Why do we need the Laws?
To condense and expand logarithms:
To Simplify!
LAWS OF LOGARITHMS
1.
log3 5  log3 x  log3 5x
When you are adding logs
2.
multiply!!
9
log 4 9  log 4 x  log 4
x
When you are subtracting logs
divide!!
LAWS OF LOGARITHMS
3.
log x  3log x
3
log x3  3log x
LAWS OF LOGARITHMS
4.
log5 x
5
x
The log and exponential are inverses of each other
so they cancel each other!
Example:
log3 2 x
3
 2x
e
ln 5
5
LAWS OF LOGARITHMS
5.
log8 8  x
x
This is because
So we get
And
log8 8
x log8 8
log8 8  1
x
Let’s Practice! (No Calculator)
Evaluate
log 3  log 6  log 5
2log12 6  log12 4
Let’s Practice! (No Calculator)
Evaluate
1
log 64  2 log 5
3
Simplify
e
1
ln x
2
Let’s Practice! (No Calculator)
3ln x
e
1
ln 4
e
Let’s Practice! (No Calculator)
10
4  log5
Express y in terms of x:
log y  5log x
Express y in terms of x:
ln y  3ln x  2ln 6
Write as a single logarithm:
2  log8 x
Solve:
log7  x  8  log7 2  2
Solve:
log 4  x  2   log 4 x  log 4 8
2
Homework:
5.6
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