Download 3.3 Properties of Logarithms – Day 1 Goal(s): • Use Change-of

3.3 Properties of Logarithms – Day 1
Goal(s):
 Use Change-of-Base property to rewrite and evaluate logarithms.
 Use properties of logarithms to expand logarithms into a sum, difference and/or
multiple of logarithms.
Lesson
What is a good estimate of log 2 10 ?
Change-of-Base Formula
Let a, b, and x be positive real numbers such that a  1, and b  1 . Then log a x can be converted to a
different base as follows.
Base b
log a x 
Ex 1.
a)
Ex 2.
a)
log b x
log b a
Base 10
log a x 
Base e
log x
log a
log a x 
Write the logarithm as a ratio of common logarithms.
b)
Write the logarithm as a ratio of natural logarithms.
b)
ln x
ln a
Properties of Logarithms
Let a be positive real number such that
then the following properties are true.
Product Rule
EXAMPLE
, and let n be a real number . If u and v are positive real numbers,
Quotient Rule
EXAMPLE
Power Rule
EXAMPLE
Corresponding Properties of Exponents
Product Rule
Ex 3.
Quotient Rule
Power Rule
Use the properties of logarithms to expand the expression as a sum, difference, and/or multiple
of logarithms. (Assume all variables are positive.)
Note: When more than one property is used do quotient 1st , product 2nd, and power 3rd .
a)
b)
d)
e)
c)
3.3 Properties of Logarithms – Day 2
Goal(s):
 Use properties of logarithms to condense logarithmic expressions into a single
logarithm.
Ex 1.
Condense the expression to the logarithm of a single quantity.
Note: Apply power property 1st , then combine logarithms using product and quotient
properties from left to right .
a)
b)
d)
e)
c)