Which of the following expressions is equivalent to log3𝑥5 ?Responseslog35+log3𝑥log subscript 3 5 plus log subscript 3 xlog35·log3𝑥log subscript 3 5 times log subscript 3 x5log3𝑥5 log subscript 3 x
Question
Which of the following expressions is equivalent to log3𝑥5 ?Responseslog35+log3𝑥log subscript 3 5 plus log subscript 3 xlog35·log3𝑥log subscript 3 5 times log subscript 3 x5log3𝑥5 log subscript 3 x
Solution
The expression equivalent to log3𝑥5 is log35+log3𝑥. This is due to the properties of logarithms, specifically the product rule which states that the log of a product is equal to the sum of the logs of its factors. In this case, 𝑥5 is the product of 5 and 𝑥, so log3𝑥5 can be written as log35+log3𝑥.
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