004 Sample Final A, Problem 15

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Solve.

Foundations
1) How can we combine the two logs?
2) How do we remove logs from an equation?
Answer:
1) One of the rules of logarithms states that
2) The definition of the logarithm tells us that if , then .

Solution:

Step 1:
Using a rule of logarithms, the equation becomes .
Step 2:
By the definition of the logarithm,
means
Step 3:
Now, we can solve for . We have .
So, there are two possible answers, which are or .
Step 4:
We have to make sure the answers make sense in the context of the problem. Since the domain of the log function is

, -9 is removed as a potential answer. The answer is .

Final Answer:

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