Lesson_8.4_LawsofLogs - Lesson_8.4_LawsofLogs.notebook 8.4...

Lesson_8.4_LawsofLogs.notebook
8.4 Laws of Logarithms
Recall: Exponent Laws
(1) Products (2) Quotients (3) Power of a Power
(a
m
)(a
n
) = a
m + n
(a
m
) ÷ (a
n
) = a
m ­ n
(a
m
)
n
= a
mn
We can derive similar laws for logarithms.
#1: Product Law for Logarithms
Determine an equivalent expression for log
a
(mn), where a , m , and
n are positive numbers and a ≠1.
Laws of Logarithms
(provided a > 0, m > 0, n > 0, and a ≠ 1)
log
a
(mn) =
log
a
(m/n) =
log
a
(m)
c
=
Example 1
Express as a single logarithm.