Richland Community College Properties of the Logarithms Expressions Questions

Only 8 simple questions one important thing is that you need to show your work.

7-6 Classwork
Properties of Logarithms
You can write a logarithmic expression containing more than one logarithm as a single
logarithm as long as the bases are equal. You can write a logarithm that contains a number
raised to a power as a logarithm with the power as a coefficient. To understand the following
properties, remember that logarithms are powers.
Name
Product Property
Formula
logo mn=logo m + logon
Why?
When you multiply two
powers, you add the
exponents.
Example: 26.22 = 26+2) = 28
When you divide two powers,
you subtract the exponents.
Example:
bo
216-2 -24
ka
Quotient Property
m
log
= logam + logan
Power Property
logam = nlogam
When you raise a power to a
power, you multiply the
exponents. Example:
(20)2 = 216-2) = 212
Problem
210g26-log29+ £ 1082 27
What is
written as a single logarithm?
1 Use the Power Property twice.
2 log2 6– log29+10g2 27
log2 62 – log2 9 + log2 273
1
62 -36, 273 = {27 – 3
= log2 36 – log2 9+ log23
Group two of the logarithms. Use
= (log236-log2 9) + log2 3 order of operations.
Quotient Property
log2
9
36 – log23
log2(3-3)
Product Property
Simplify
_log212
2 log2 6 – log29+ log2 27
As a single logarithm,
log212
=
Name
Class
Date
7-6 Classwork (continued)
Properties of Logarithms
To evaluate logarithms with any base, you can rewrite the logarithm as a quotient of
two logarithms with the same base.
logo
Move the base
to the bottom.
logo
log.
Move the number
to the numerator.
Problem
What is logu 8 written as a quotient of two logarithms with base 22 Simplify your answer,
if possible.
log. 8
The base is 4 and the number is 8. Move the base to the bottom and
the number to the numerator.
log, 8
log, 4
3
2
Evaluate the logarithms in the numerator and the denominator.
Write each logarithmic expression as a single logarithm.
1. log:13 + log: 3
2. 4 log x + 3 log x
3. log2 x + log2 y
4. 5 log 3 + log 4
5. logs x + 3 logs y
6. log2 16 – log2 8
Write each logarithm as a quotient of two common logarithms. Simplify your
answer, if possible. (Hint: Common logarithms are logarithms with base 10.)
7. loge 12
8. logs 16