Use the quotient property:

\(log_b (\frac{m}{n})=\log_b m-\log_b n\):

\(=\log_3 1-\log_3 27x^{2}\)

The logarithm of 1 (using any base) is 0:

\(=0-\log_3 27x^{2}\)

\(= -\log_3 27x^{2}\)

Use the product property: \(\log_b mn=\log_b m+\log_b n\):

\(= -(\log_3 27+\log_3x^{2})\)

\(= -(\log_3 3^{3}+log_3x^{2})\)

Use the rule: \(\log_b b^{x}=x\):

\(= -(3+\log_3x^{2})\)

\(= -3-\log_3x^{2}\)

Use the power property: \(\log_bx^{n}=n\log_bx\)

\(= -3-2\log_3x\)