Exponential Functions And Logarithms Worksheet Page 4
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1
2
3
4Logarithm of a Product
Example #1: Rewrite as a sum.
log
(xy) = log
x + log
y
log(21) =
b
b
b
Logarithm of a Quotient
Example #2: Rewrite as a difference.
x
y
log
(
) = log
x – log
y
log
=
b
b
b
3
y
8
Logarithm of a Power
Example #3: Rewrite as a ‘linear’ log expression.
n
log
(x
) = n log
x
log
3
x =
b
b
a
Change of Base Formula
Example #4: Evaluate the logarithm.
log b
log
b =
log
23 =
a
5
log a
Examples:
1. Without a calculator! Find log 15 given
2. Without a calculator! Find log 48 given
log 3 ≈ .47712 and log 5 ≈ .69897
log 2 ≈ .301 and log 3 ≈ .477
3. Express the following as a single logarithm:
1
log
3 + 2 log
5
5log
m – log
p
log
x -
log
y
7
7
2
2
5
5
5
4. Simplify each expression completely.
5
!
$
1
1
log
32 – log
42
log
27 + log
log
49 ! log
7
log
#
&
2
2
1
1
7
7
2
9
"
2
%
3
3
5. Evaluate the logarithmic expressions.
log
39 =
log
95 =
6
3
Assignment: Page 253, 17-29 odd, 39-43, Page 260, 21-35 odd, 41-45 odd, 66-68
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