Given the equation:
[tex]f(x)=\log _4x[/tex]
the given equation is for logarithm function with a base of 4
The domain will be all real numbers of x
So,
[tex]Domain=(0,\infty)[/tex]
We will find the value of f(2)
So, substitute with x = 2 and solve
so,
[tex]\begin{gathered} f(2)=\log _42 \\ 2=\sqrt[]{4}=4^{\frac{1}{2}} \\ \\ f(2)=\log _42=\log _44^{\frac{1}{2}}=\frac{1}{2}\cdot\log _44=\frac{1}{2}\cdot1=\frac{1}{2} \end{gathered}[/tex]
So, the answer will be:
[tex]f(2)=\frac{1}{2}[/tex]
