Answer:
[tex]y=\log _{\frac{1}{4}}\left(x\right)[/tex]
Step-by-step explanation:
The function that belong to the graph is the second one:
[tex]y=\log _{\frac{1}{4}}\left(x\right)[/tex]
We deduct from the properties of logarithmic functions. When the base is between 0 and 1, the function will decrease, and 1 divided by 4 is in this interval, also the graph is showing a decrease. Therefore, the function with base [tex]\frac{1}{4}[/tex] is the answer.
However, we have to options, but one of them has a negative argument, which cannot represent the graph, because that negative means a reflection across y-axis, and the given graph is not reflected.
Therefore, the correct answer should your included a decrease behaviour, which is:
[tex]y=\log _{\frac{1}{4}}\left(x\right)[/tex]
(Also, the actual graph is attached, you can see that's the same)
