what happens to the value of $f(x)=log_4x$ as $x$ approaches $+infty$?
what happens to the value of $f(x)=log_4x$ as $x$ approaches $+infty$?
Answer
Explanation:
Step1: Recall log - function property
The logarithmic function (y = \log_{a}x) ((a>1)) is an increasing function. Here (a = 4>1) and (y=\log_{4}x).
Step2: Analyze the limit
As (x\to+\infty), for the function (y = \log_{4}x), we consider the limit (\lim_{x\to+\infty}\log_{4}x). Since the function is increasing without bound as (x) gets larger and larger, the value of (\log_{4}x) also increases without bound.
Answer:
(f(x)\to+\infty)