008A Sample Final A, Question 16

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Question: Solve.

1) How do we combine the two logs?
2) How do we remove the logs?
1) One of the rules of logarithms says that
2) The definition of logarithm tells us that if , then


Step 1:  
Using one of the properties of logarithms the, left hand side is equal to
Step 2:  
By the definition of logarithms means
Step 3:  
Now we do some arithmetic to solve for x. . So there are two possible answers.
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   ,   -3 is removed as a potential answer.
Final Answer:  
x = 4.

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