what happens to the value of $f(x)=log_4x$ as $x$ approaches 0 from the right?

Explanation:

Step1: Recall logarithm property

The function $y = \log_{a}x$ is equivalent to $a^{y}=x$ ($a>0,a\neq1,x > 0$). For $y=\log_{4}x$, we have $4^{y}=x$.

Step2: Analyze the limit

As $x$ approaches $0$ from the right ($x\rightarrow0^{+}$), we consider the equation $4^{y}=x$. We need to find what $y$ (i.e., $f(x)$) does. Since $4^{y}$ is an exponential - function with base $a = 4>1$, as $x$ gets smaller and smaller positive values, $y$ must decrease without bound. Mathematically, $\lim_{x\rightarrow0^{+}}\log_{4}x=-\infty$.

Answer:

The value of $f(x)$ approaches negative infinity.