Using translation concepts, it is found that function g(x) is given by:
[tex]g(x) = \frac{1}{5}\log_{2}{x} - 4[/tex]
What is a translation?
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the parent function is given by:
[tex]f(x) = \log_{2}{x}[/tex]
It was shifted 4 units down, hence:
[tex]g(x) = \log_{2}{x} - 4[/tex]
It was vertically compressed by a factor of 0.2, hence:
[tex]g(x) = \frac{1}{5}\log_{2}{x} - 4[/tex]
More can be learned about translation concepts at https://brainly.com/question/4521517
