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What is the expanded form of log<sub>2</sub>(27x<sup>2</sup>)?

24. What is the expanded form of log<sub>2</sub>(27x<sup>2</sup>)?
a. 3 + 2log<sub>2</sub>(x)
b. 3 + log<sub>2</sub>(2x)
c. 2 + 3log<sub>2</sub>(x)
d. 27 + 2log<sub>2</sub>(x)

Answer

Answer: a. 3 + 2log2(x)

Explanation: log2(27x2) can be expanded using the properties of logarithms: log2(27) + log2(x2). Since 27 = 33, log2(27) = 3log2(3). Therefore, the expression becomes 3 + 2log2(x).

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