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Transcript
4-3
Day 1
Properties of Logarithms
The Product Rule
Let b, M, and N be positive real numbers with b  1.
The logarithm of a product is the sum of the logarithms.
Example 1: Use the product rule to expand each logarithmic expression.
a) log 6 7  11
b) log 100x
c) log 7 x 
The Quotient Rule
Let b, M, and N be positive real numbers with b  1.
The logarithm of a quotient is the difference of the logarithms.
Example 2: Use the quotient rule to expand each logarithmic expression.
 e5 
x
 23 
a) log
b) log 8  
c) ln  
2
 x 
 11 
The Power Rule
Let b and M be positive real numbers with b  1, and let p be any real
number.
The logarithm of a number with an exponent is the product of the exponent
and the logarithm of that number.
Example 3: Use the power rule to expand each logarithmic expression.
a) ln x 2
b) log 6 39
c) ln 3 x
Example 4: Use logarithmic properties to expand each expression as much
as possible:
 3 x 

a) log b x 2 y
b) log 6 
4 
36
y




c) log b x

43
y

d) log 2
5
xy 4
16
Practice: Use logarithmic properties to expand each expression as much as
possible
 x
 64 

1) log b xy3 
2) log 5 
3) log 8 


 x 1 
 25 
 x3 y 
4) log b  2 
 z 
 3 xy4
7) log b  5
 z
5) ln ex




6) log 5
8) log 5
x
25 y 3
x
y