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Exponential and Logarithmic Functions:
log
a
y
xy
a
x
=⇔ =
ln log , ln
xx
e
e
==
where
1
ln
x
=⇔=
e
y
__________________________________________________________
Laws of Logs:
1.
log log log
aa
a
MN M N
=+
2.
log
log
log
a
M
N
MN
=
3.
log log
a
p
a
Mp
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
+
(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
(
29
Law 1 involves a
product
in the ARGUMENT of a single
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This note was uploaded on 12/11/2011 for the course MAC 1140 taught by Professor Kutter during the Fall '11 term at FSU.
 Fall '11
 Kutter
 Algebra, Logarithmic Functions

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