Exponential and Logarithmic Functions:
log
a
y
x
y
a
x
=
⇔
=
ln
log
,
ln
x
x
e
e
=
=
where
1
ln
x
y
x
=
⇔
=
e
y
__________________________________________________________
Laws of Logs:
1.
log
log
log
a
a
a
MN
M
N
=
+
2.
log
log
log
a
a
a
M
N
M
N
=

3.
log
log
a
p
a
M
p
M
=
(
This law can be very useful in solving equations which have an
unknown in the exponent of an expression.)
____________________________________
Be Careful:
The above Laws of Logs do
not apply to the following.
Why?
log
a
M
N
+
(
29
(
Law 1 involves the
sum of two different log terms.
This
has a
sum in the ARGUMENT of a single log term.
)
log
log
a
a
M
N
(
29(
29
(
Law 1 involves a
product
in the ARGUMENT of a single
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 Fall '11
 Kutter
 Algebra, Logarithmic Functions, Natural logarithm, Logarithm, different log terms

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