Log Functions
Definition: For b > 0, b not equal to 1,
=
is equivalent to
=
The logarithm is the exponent needed on the base b in order to get the number x.
Examples:
=
is equivalent to
=
=
is equivalent to
=
Theorem 1: Properties of Logarithms:
If b, M, and N are positive reals with b not equal to 1, and p and x are any reals, then:
1)
=
5)
=
+
2)
=
6)
=

3)
=
7)
=
4)
=
8)
=
if and only if
=
for x > 0 only
Common Errors:
1)
is not

The latter is
2)
is not
+
The latter is
3)
(
)
is not
The latter is