Answer:
Option C.
Step-by-step explanation:
There are three points which are passing through the logarithmic function shown in the graph.
The points are (0.4, -0.6), (1, 0) and (3, 1).
Now we will plug in the values (3, 1) in all the options to get the correct answer.
a). [tex]y=log_{0.4}x[/tex]
We can rewrite the equation as
[tex](0.4)^{y}=x[/tex] [If [tex]a^{b}=c[/tex] then [tex]b=log_{a}c[/tex]]
For (3, 1)
[tex](0.4)^{1}=3[/tex]
Which is not true so option A is not the answer.
b). [tex]y=log_{1}x[/tex]
We can rewrite the equation as
[tex](1)^{y}=x[/tex]
For (3, 1)
[tex](1)^{3}=3[/tex]
1 = 3
Which is not true.
Therefore, Option B is not the answer.
c). [tex]y=log_{3}x[/tex]
We can rewrite the equation as
[tex](3)^{y}=x[/tex]
For (3, 1)
[tex](3)^{1}=3[/tex]
3 = 3
Therefore, option C is the answer.
d). [tex]y=log_{10}x[/tex]
We can rewrite the equation as
[tex](10)^{y}=x[/tex]
For (3, 1)
[tex](10)^{1}=3[/tex]
Not true. Therefore, option D is not the answer.
