Question

Write as the sum and/or difference of logarithms. Express powers as factors.

Answer 1

From logarithms properties, we have:

`\begin{gathered} \log _a((B_1)/(B_2))=\log _aB_1-\log _aB_2 \\ \log _a(B^c)=c*\log _aB \end{gathered}`

Applying these properties in the given expression, we have:

`\begin{gathered} \log _2((x^3)/(y^7))=\log _2x^3-\log _2y^7 \\ \log _2((x^3)/(y^7))=3\log _2x-7\log _2y \end{gathered}`

From the solution developed above, we are able to conclude that the correct answer is the third one.