Let's analyze each of the given options to determine which one represents a logarithmic function.
1. [tex]\( y = 0.25x \)[/tex]
This is a linear function because it follows the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept. In this case, [tex]\( m \)[/tex] is 0.25 and [tex]\( b \)[/tex] is 0.
2. [tex]\( y = x^{0.25} \)[/tex]
This is a power function because it follows the form [tex]\( y = x^a \)[/tex], where [tex]\( a \)[/tex] is a constant. Here, [tex]\( a \)[/tex] is 0.25.
3. [tex]\( y = \log_{0.25} x \)[/tex]
This is a logarithmic function, as it follows the form [tex]\( y = \log_b x \)[/tex], where [tex]\( b \)[/tex] is the base of the logarithm. In this case, the base [tex]\( b \)[/tex] is 0.25.
4. [tex]\( y = (0.25)^x \)[/tex]
This is an exponential function because it follows the form [tex]\( y = a^x \)[/tex], where [tex]\( a \)[/tex] is a constant. Here, the base [tex]\( a \)[/tex] is 0.25.
After reviewing and analyzing all four options, the correct answer—a function that is logarithmic—is:
[tex]\[ y = \log_{0.25} x \][/tex]
Thus, the function that is logarithmic is:
[tex]\[ y = \log_{0.25} x \][/tex]
So, the correct choice is option 3.
