Question

Given the base function y= log2(base)X. Rewrite y = log2(base) square root of X over 4 as the transformation of the base function.

Answer 1

Answer:
`\begin{gathered} y=2\log _2x-2 \\ \text{where }\log _2x\text{ is the base function} \end{gathered}`Step-by-step explanation:

Let the base function be:

`f(x)=\log _2x`

The second function is:

`y=\log _2\frac{\sqrt[]{x}}{4}`

This can be re-written as:

`\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}`

Note that:

`\begin{gathered} \log _22=1 \\ \end{gathered}`

The resulting transformed expression therefore becomes:

`\begin{gathered} y=2\log _2x-2(1) \\ y=2\log _2x-2 \end{gathered}`