From logarithms properties, we have:
[tex]\begin{gathered} \log _a(\frac{B_1}{B_2})=\log _aB_1-\log _aB_2 \\ \log _a(B^c)=c\times\log _aB \end{gathered}[/tex]
Applying these properties in the given expression, we have:
[tex]\begin{gathered} \log _2(\frac{x^3}{y^7})=\log _2x^3-\log _2y^7 \\ \log _2(\frac{x^3}{y^7})=3\log _2x-7\log _2y \end{gathered}[/tex]
From the solution developed above, we are able to conclude that the correct answer is the third one.
