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Exercise: Use the properties of logarithms to expand the expression listed below. Each logarithm should involve only one variable and should not have any radicals or exponents. Assume that all variables represent positive real numbers.
\[
\log _{2}\left(\frac{8 x}{\sqrt[3]{y}}\right)
\]

Step 1 ：Apply the property of logarithms \(\log_b(M/N) = \log_b(M) - \log_b(N)\) to the given expression: \(\log _{2}(8x) - \log _{2}(\sqrt[3]{y})\)

Step 2 ：Apply the property of logarithms \(\log_b(MN) = \log_b(M) + \log_b(N)\) to the first term: \(\log _{2}(8) + \log _{2}(x) - \log _{2}(\sqrt[3]{y})\)

Step 3 ：Apply the property of logarithms \(\log_b(M^p) = p \cdot \log_b(M)\) to the first and last term: \(3 \cdot \log _{2}(2) + \log _{2}(x) - \frac{1}{3} \cdot \log _{2}(y)\)

Step 4 ：Simplify the expression, since \(\log _{2}(2) = 1\), the expression simplifies to: \(3 + \log _{2}(x) - \frac{1}{3} \cdot \log _{2}(y)\)

Step 5 ：So, the expanded form of the given logarithmic expression is \(\boxed{3 + \log _{2}(x) - \frac{1}{3} \cdot \log _{2}(y)}\)