To determine which of the given options is a logarithmic function, we need to understand the form of a logarithmic function. A logarithmic function can be generally expressed as [tex]\( y = \log_a x \)[/tex], where [tex]\( a \)[/tex] is the base of the logarithm.
Let's analyze each option:
1. [tex]\( y = 0.25x \)[/tex]: This is a linear function because the variable [tex]\( x \)[/tex] is to the first power and it has a constant coefficient of 0.25. It does not have the form of a logarithmic function.
2. [tex]\( y = x^{0.25} \)[/tex]: This is a power function. The exponent 0.25 is applied to the variable [tex]\( x \)[/tex]. It is not a logarithmic function.
3. [tex]\( y = \log_{0.25} x \)[/tex]: This is a logarithmic function because it is in the form [tex]\( y = \log_a x \)[/tex], with the base [tex]\( a \)[/tex] being 0.25.
4. [tex]\( y = (0.25)^x \)[/tex]: This is an exponential function because the base 0.25 is raised to the power of [tex]\( x \)[/tex]. It is not a logarithmic function.
Thus, the logarithmic function among the given options is:
[tex]\[ y = \log_{0.25} x \][/tex]
Therefore, the correct option is:
[tex]\[ y = \log_{0.25} x \][/tex]
