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Explanation:

Using the properties of logarithms, the left side of the equation becomes

$\log{3x^3} - \log{x^2} = \log{3x}$

while the right hand side becomes

$\log{27} - \log{x} = \log{(27)/(x)}$

so we end up with

$3x^2 =27 \Rightarrow x = 3$

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