Answer:[tex]\begin{gathered} y=2\log _2x-2 \\ \text{where }\log _2x\text{ is the base function} \end{gathered}[/tex]Explanation:
Let the base function be:
[tex]f(x)=\log _2x[/tex]
The second function is:
[tex]y=\log _2\frac{\sqrt[]{x}}{4}[/tex]
This can be re-written as:
[tex]\begin{gathered} y=\log _2\sqrt[]{x}-\log _24 \\ y=\log ^{}_2x^2-\log _22^2 \\ y=2\log _2x-2\log _22 \end{gathered}[/tex]
Note that:
[tex]\begin{gathered} \log _22=1 \\ \end{gathered}[/tex]
The resulting transformed expression therefore becomes:
[tex]\begin{gathered} y=2\log _2x-2(1) \\ y=2\log _2x-2 \end{gathered}[/tex]
