Name:
Date:
Period:
Independent Practice 9.2 Properties of Logarithms
1)
1.
2.
3.
Condense: log 8 − 2 log 6 + log 3
Use power property first. Are there any
number being multiplied to a log? That
number (2) becomes the exponent of 6
Positive sign means log belong in numerator
and negative sign means logs belong
denominator.
Simplify if needed
Answer
2) Condense:
log
(log 2 + log
) − 3 log
1.
Distribute the to both logs inside the
parentheses
2.
Use power property first. Are there any number
being multiplied to a log? That number
becomes the exponent of 2 and y
3.
Positive sign means numerator and negative
sign means denominator.
4.
Simplify if needed
Answer
3) Condense:
log
log
+ log
2
3
2
− log
1. Use power property first. Are there any number
being multiplied to a log?
2. Positive sign means numerator and negative sign
means denominator.
3. Simplify if needed
Answer
4) Expand log
log
∗√
√
1. Write any radical as an exponent. √7 =?
2. Values in the numerator expand with positive
signed log and values in the denominator expand
with negative exponents. There should be 3 log
terms
3. The exponents become the number multiplied in
front of log
Answer
1
log + log 7 − 2 log
2
5) Expand
(2 )
1. Use exponent rule and apply exponent 2 to the 2
values in the parentheses
2. Values in the numerator expand with positive
signed log and values in the denominator expand
with negative exponents.
3. The exponents become the number multiplied in
front of log
2
Answer
2+2
6) Expand log 3
1. Values in the numerator expand with positive
signed log and values in the denominator expand
with negative exponents. You should split log for
values 3,
, and
2. The exponents become the number multiplied in
front of log. Must change sign of log when using the
power property and have a negative exponent.
Answer is the quotient
7) Evaluate
4+
log 3 + 4 log
9
1. Condense the log
2. Write in exponential form, remembering logs
equal exponents and this is what you are trying to
find.
Answer
7) Evaluate
2
1−
100
1. Condense the log
2. Write in exponential form, remembering logs
equal exponents and this is what you are trying to
find.
Answer
-2
− 2 log