Question

use a graph or a table to find the following limit.
lim log₄(x)
x→0⁺
lim log₄(x) = (simplify your answer.)
x→0⁺

Explanation:

Step1: Recall the property of logarithmic functions

The function $y = \log_{a}x$ where $a>1$ (here $a = 4$) has the following behavior. As $x$ approaches $0$ from the right - hand side, the value of $\log_{a}x$ decreases without bound.
Let's consider the general form of the logarithmic function $y=\log_{a}x$, which is the inverse of the exponential function $x = a^{y}$. When $x$ gets closer and closer to $0$ from the positive side, we are looking for $y$ such that $a^{y}=x$. As $x
ightarrow0^{+}$, $y
ightarrow-\infty$.

Step2: Apply to the given function

For the function $y = \log_{4}x$, as $x
ightarrow0^{+}$, the value of $\log_{4}x$ approaches $-\infty$.

Answer:

$-\infty$