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Math 030 - Cooley
Intermediate Algebra
OCC
Section 9.4 – Properties of Logarithmic Functions
The Product Rule For Logarithms
For any positive numbers M, N, and a ( a  1 ),
log a ( MN )  log a M  log a N
(The logarithm of a product is the sum of the logarithms of the factors.)
The Quotient Rule For Logarithms
For any positive numbers M, N, and a ( a  1 ),
log a
M
 log a M  log a N
N
(The logarithm of a quotient is logarithm of the dividend minus the logarithm of the divisor.)
The Power Rule For Logarithms
For any positive numbers M and a ( a  1 ), and any real number p,
loga M p  p  loga M
(The logarithm of a power of M is the exponent times the logarithm of M.)
The Logarithm Of The Base To An Exponent
For any base a,
loga (a)k  k
(The logarithm, base a, of a to an exponent is the exponent.)
 Exercises:
Express as an equivalent expression that is a sum of logarithms.
1)
log 2 (16  32)
2)
logt (3ab)
Express as an equivalent expression that is a single logarithm.
3)
logb 5  logb 9
4)
logt H  log t M
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Math 030 - Cooley
Intermediate Algebra
OCC
Section 9.4 – Properties of Logarithmic Functions
 Exercises:
Express as an equivalent expression that is a difference of two logarithms.
5)
29
log3 13
6)
log a
y
x
Express as an equivalent expression that is a single logarithm.
7)
logb 3  logb 32
8)
log a 26  log a 2
10)
log c M 4
Express as an equivalent expression that is a product.
9)
log b t 5
Express as an equivalent expression, using the individual logarithms of w, x, y, and z.
11)

log a x 2 y5

12)
log a
x4
13)
yz 2
log c
x8 y12
c3 z 5
Express as an equivalent expression that is a single logarithm and, if possible, simplify.
13)
3logc p  12 logc t  logc 7
14)
1 log 2 x  3(log
a
a
2
x  loga y)
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