Download ln 7x log 7 5 • log 10x ln 11 e x =

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Pre-Calculus
3.3 Properties of Logs
pgs.441 - 450
Product Rule

Previously we learned properties of exponents such as the following:
x 2  x3 
Similarly we have the product rule when we use logarithms.
Let b, M, and N be positive real numbers with _____________________
The logarithms of a ________________ is the _____________ of the ___________________________.
Example 1
(a)
ln 7x 
Expand the Logs using the product rule.
(b)
log 4 7  5
(c)
log 10x 
Quotient Rule

Previously we learned properties of exponents such as the following:
x7

x4
Similarly we have the product rule when we use logarithms.
Let b, M, and N be positive real numbers with _____________________
The logarithms of a ________________ is the _____________ of the ___________________________.
Example 2
x

2
(a) log 5 
Expand the Logs using the quotient rule.
 19 

 x 
(b) log 7 
(c)
 e3 
ln  
 11 
Power Rule

Previously we learned properties of exponents such as the following:
x 
5 3

Similarly we have the product rule when we use logarithms.
Let b, M, and N be positive real numbers with _____________________
The logarithms of a ____________________ with an __________________________is the _________________ of the
___________________ and the logarithm of that number.
1
Expand the Logs using the power rule.
Example 3
(a)
ln x 2
(b) log 5 7
4
(c) ln
(d) log  4x 
5
x
Expanding Logarithmic Expressions
It is sometimes necessary to use more than one of the properties of logs when you expand. Notice any from the previous
example?
Let’s try expanding out logs that have more than one property!
Example 4

log b x 2 y
Example 5

 3x
log 6 
4
 36 y



Page 449 prob 1 – 40
Condensing Logs
We can also go backwards!!!!
Let’s try condensing logs that have more than one property!
Example 6
Example 7
log 4 2  log 4 32
log  4 x  3  log x
Page 449 prob 41 – 70
2
The Change-of-Base
For any log bases a and b, and any posistive M…
Change-of-Base
Introducing Common Logs
Introducing Natural Logs
Use the common log and natrual log to change the base of the given functions
Example 8
Example 9
log 5 140
log7 2506
Page 449 prob 71 – 76
3