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Which expression is equivalent to log3(x + 4)?
A. log3 – log(x + 4)
B. log12 + logx
C. log3 + log(x + 4)
D. log 3/log(x+4)
CORRECT ANSWER: C
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log[3(x+4)] is equal to log(3) + log(x + 4), which corresponds to choice number three.
By the logarithm product rule, for two nonzero numbers and ,
Keep in mind that a logarithm can be split into two only if the logarithm contains the product or quotient of two numbers.
For example, is the number in the logarithm . Since is a product of the two numbers and , the logarithm can be split into two. By the logarithm product rule,