RULES OF LOGARITHMS - RULE 3
RULES OF LOGARITHMS - RULE 3 
Let a be a positive number such that a does not equal 1, let
n be a real number, and let u and v be positive real numbers.
Logarithmic Rule 3: 
.
Example 1: Find 
two ways.
Solution: Since 
can be written 
, the
expression can be written
which in turn can be written
We have
and
Example 2: Find 
.
Solution: The expression can be
written 
which in turn can be written 
. This last expression can be
rewritten using Rule 1 as
This represents 6 identical terms and we can
write the sum of the six terms as 
.
Check: The original expression can be written
The last expression can be written
If you would like to review another example, click on Example.
Work the following problems and if you want to check your answer, click on answer.
Problem 1: Find 
Problem 2: Find 
Problem 3: Simplify 
Problem 4: Simplify 
Problem 5: Simplify 
Problem 6: Simplify 
. What assumptions must you make before you can begin work on this problem?
Problem 7: Simplify the following term completely
State the domain that makes your final answer equal to the original expression.
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Author: Nancy Marcus