LOGARITHMIC
PROPERTY DAY!!!!
8.4 – Properties of Logarithms
Properties of Logarithms


There are four basic properties of
logarithms that we will be working with.
For every case, th...
Product Rule
logbMN = LogbM + logbN



Ex: logbxy = logbx + logby



Ex: log6 = log 2 + log 3



Ex: log39b = log39 + l...
Quotient Rule
log







Ex: log

Ex: log
Ex: log

M
b

5
MN

2

P

M

log

5

x

log

log

2

a

log

y

a
2

b

N

x
...
Power Rule
log



Ex: log



Ex:



Ex: log

5

log

2

B

2

5

x

3

7

M

b

a b

4

x

x log

2 log
x log
3 log

5
...
Let’s try some


Working backwards now: write the following as a single
logarithm.

log 4 4

log 4 16

log 5

log 2

2 lo...
Let’s try some


Write the following as a single logarithm.

log 4 4

log 4 16

log 5

log 2

2 log 2 m

4 log 2 n
Let’s try something more
complicated . . .
Condense the logs
log 5 + log x – log 3 + 4log 5

log 4 5

2 log 4 x

5 (log 4 ...
Let’s try something more
complicated . . .
Condense the logs
log 5 + log x – log 3 + 4log 5

log 4 5

2 log 4 x

5 (log 4 ...
Let’s try something more
complicated . . .


Expand
log

10 x
3y

3

4

2

log

2 x
8

5
Let’s try something more
complicated . . .


Expand
log

10 x
3y

3

4

2

log

2 x
8

5
8.4 properties of logarithms
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8.4 properties of logarithms

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8.4 properties of logarithms

  1. 1. LOGARITHMIC PROPERTY DAY!!!! 8.4 – Properties of Logarithms
  2. 2. Properties of Logarithms  There are four basic properties of logarithms that we will be working with. For every case, the base of the logarithm can not be equal to 1 and the values must all be positive (no negatives in logs)
  3. 3. Product Rule logbMN = LogbM + logbN  Ex: logbxy = logbx + logby  Ex: log6 = log 2 + log 3  Ex: log39b = log39 + log3b
  4. 4. Quotient Rule log    Ex: log Ex: log Ex: log M b 5 MN 2 P M log 5 x log log 2 a log y a 2 b N x 5 log log 2 M log b N y 5 2 5 log 2 N log 2 P
  5. 5. Power Rule log  Ex: log  Ex:  Ex: log 5 log 2 B 2 5 x 3 7 M b a b 4 x x log 2 log x log 3 log 5 b M B 2 5 7 a 4 log 7 b
  6. 6. Let’s try some  Working backwards now: write the following as a single logarithm. log 4 4 log 4 16 log 5 log 2 2 log 2 m 4 log 2 n
  7. 7. Let’s try some  Write the following as a single logarithm. log 4 4 log 4 16 log 5 log 2 2 log 2 m 4 log 2 n
  8. 8. Let’s try something more complicated . . . Condense the logs log 5 + log x – log 3 + 4log 5 log 4 5 2 log 4 x 5 (log 4 3 x log 4 5 x )
  9. 9. Let’s try something more complicated . . . Condense the logs log 5 + log x – log 3 + 4log 5 log 4 5 2 log 4 x 5 (log 4 3 x log 4 5 x )
  10. 10. Let’s try something more complicated . . .  Expand log 10 x 3y 3 4 2 log 2 x 8 5
  11. 11. Let’s try something more complicated . . .  Expand log 10 x 3y 3 4 2 log 2 x 8 5

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