Question

Which of the following is equivalent to log( 1/9k )?

A)−log(9k)
B) 1/ log(9k)
C)−log(3k)
D) 1/ 3log(k)

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Answer 1

`\Large \textsf{Read below}`

Step-by-step explanation:

`\Large \text{$ \sf log\left((1)/(9k)\right) = log\:1 - log\:9k$}`

`\Large \text{$ \sf log\left((1)/(9k)\right) = 0 - log\:9k$}`

`\Large \text{$ \sf log\left((1)/(9k)\right) = - log\:9k$}`

Answer 2

The equivalent expression for log(1/9k) is -log(9k), which is option A. This is found by applying the properties of logarithms that allow us to convert a log division into a subtraction, and therefore the negative log of the product 9k.

Step-by-step explanation:

The student has asked to find an equivalent expression for log(1/9k). Using logarithmic properties, we can rewrite this expression as the negative of the logarithm, since the original value is a fraction. Thus, using the log rule log(a/b) = log(a) - log(b), the expression becomes -log(9k).

Therefore, the equivalent expression is -log(9k), which corresponds to option A. It cannot be option B, C, or D because those don't correctly apply the logarithm rules to the original question.

Option B inverses the entire expression incorrectly, option C loses the square of 3 which is 9, and option D incorrectly distributes the logarithm and the fraction.