Work each problem. Which of the following is equivalent to 2 ln(3...

Question

Work each problem. Which of the following is equivalent to 2 ln(3x) for x > 0?
A. ln 9 + ln x B. ln 6x C. ln 6 + ln x D. ln 9x^2

Accepted Answer

Hello, everyone. We are asked which of the following logarithmic expressions is equivalent to three times the natural log of nine X note that X is greater than zero. Our answer choices are a, the natural log of 729 plus the natural log of X B. The natural log of 729 X cubed C the natural log of 27 X D, the natural log of 27 plus the natural log of X. First, I'm going to rewrite my expression. So I have three multiplied by the natural log of in parentheses nine XX. I recall that if I have a coefficient on a logarithm, I can rewrite that as the exponent of the number behind the logarithm. So this is gonna get rewritten as the natural log of in parentheses nine X cubed. Next, recalling my exponent rules. I don't do that if I have an exponent on a set of parentheses, this is the same as saying that exponent is on both bases within the parentheses. So I can say the natural log of nine cubed X cubed in parentheses from there, I'm going to expand nine cubed. So I now have the natural log of 729 X cubed. And it's still in parentheses because that goes with the natural logs. We want to keep it all together from there. There does not appear to be anything else I can do to simplify this. So the natural log of 729 X cubed is my answer. And that's answer. Choice B have a nice day.

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Work each problem. Which of the following is equivalent to 2 ln(3x) for x > 0? A. ln 9 + ln x B. ln 6x C. ln 6 + ln x D. ln 9x^2