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Important Formulas for Test 2 Material
Instructor: Ms. Hoa Nguyen
(nguyen@scs.fsu.edu)
•
log
a
(
M
·
N
) =
log
a
M
+
log
a
N
(log of product = sum of logs)
•
log
a
(
M
N
) =
log
a
M

log
a
N
(log of quotient = diﬀerence of logs)
•
log
a
M
r
=
rlog
a
M
(Power can be brought to the front of the log).
•
log
a
a
M
=
M
•
a
log
a
M
=
M
•
Changeofbase formula:
log
a
b
=
log
r
b
log
r
a
(i.e., changed from base
a
to base
r
).
•
1
x
m
=
x

m
(When moving from the denominator to numerator, the SIGN of the power
changes to the opposite sign).
•
ln
1
a
=
lna

1
=

lna
•
lna
lnb
+ 1 =
lna
lnb
+
lnb
lnb
=
ln
(
a
·
b
)
lnb
•
log
a
M
is DEFINED when
a >
0
, a
6
= 1 and
M >
0.
•
log
a
M
=
log
a
N
⇒
M
=
N
•
a
M
=
a
N
⇒
M
=
N
•
log
a
M
=
N
⇒
M
=
a
N
(circle trick)
•
a
M
=
N
⇒
log
a
a
M
=
log
a
N
⇒
M
=
log
a
N
•
The compound interest formula (compound in “period”) is given by
A
=
P
(1 +
r
n
)
nt
where
–
A
= Amount (Future Value)
–
P
= Principal (Present Value)
–
r
= annual rate of interest (in decimal form)
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 Spring '11
 Nuegyen
 Formulas

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