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Which of the following is the simplified version of one–half log 3 x – 2 log 3 y + 4 log 3 z? a)log 3 square root of x over y squared times z to the fourth power b)log 3 square root of x times y squared over z to the fourth power c)log 3 square root of x times z to the fourth power over y squared d)log 3 x3yz

Mathematics
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Are you familiar with the properties of logarithms? \[\log_{b} (m*n) = \log_{b} m + \log_{b}n \] \[\log_{b}(m/n) = \log_{b}m - \log_{b}n \] \[\log_{b}m ^{x} = x \log_{b} m \]
yes but I tried each of the 4 potential answers and I keep getting the wrong answer. I think it might be the last one.
Start by applying the third property to all applicable logs, so \[2\log_{3} y = \log_{3} y ^{2}\]

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Other answers:

ah let me check
the answer is in the list, maybe your mistake was you got \[\log_{3}\frac{ \sqrt{x} }{ y ^{2}z ^{4} }\] ??
I just tried it again.... the equations you gave me helped!! I see what I did wrong, of course it was simple miscalculation :p
cool glad you got it :)
thank you!

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