004 Sample Final A, Problem 15

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


Step 1:
Using a rule of logarithms, the equation becomes .
Step 2:
By the definition of the logarithm,
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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