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Section 5.3
Properties of Logarithms
Exponential/Logarithmic Forms Property
Definition
Introduction
Property
For a > 0, b > 0, b ≠ 1, the equations
logb  a   c and bc  a
are equivalent.
Section 5.3
Lehmann, Intermediate Algebra, 4ed
Slide 2
Power Property for Logarithms
Power Property for Logarithms and of Equality
Property
For x > 0, b > 0 and, b ≠ 1
logb  x p   p logb  x 
In words: A logarithm of a power of x is the
exponent times the logarithm of x.
Property
For positive real numbers a, b, and c where b ≠ 1,
the equations
a  c and log b  a   log b  c 
are equivalent.
Section 5.3
Lehmann, Intermediate Algebra, 4ed
Slide 3
Power Property for Logarithms
Solving an Exponential Equation
Example
Solve the equation 2  12.
x
Solution
Check solution: 23.5850  12.003  12
Section 5.3
Lehmann, Intermediate Algebra, 4ed
Slide 4
Power Property for Logarithms
Solving an Exponential Equation
Warning
Watch parenthesis:
Section 5.3
Lehmann, Intermediate Algebra, 4ed
Slide 5
Power Property for Logarithms
Solving an Exponential Equation
Example
Solve 3  4   71.
x
Solution
Section 5.3
Lehmann, Intermediate Algebra, 4ed
Slide 6
Power Property for Logarithms
Solving an Exponential Equation
Solution Continued
Check solution: 3  4 
Section 5.3
2.2824
 71.0008  71
Lehmann, Intermediate Algebra, 4ed
Slide 7