Question

4.3) Consider the following function. (If an answer does not exist, enter DNE.) f(x) = ln(4 − ln(x)) (a) Find the vertical asymptote(s). (Enter your answers as a comma-separated list.) x =

Answer 1

Answer: $x=0\text{ and }x=e^4$

Step-by-step explanation:

• The vertical asymptote is at the zero of the argument and at points where the argument approaches to ∞ .

Given function: $f(x) = \ln(4 - \ln(x))$

Since, $\ln 0=\infty$

Here, if

$f(x)\to \infty\\\Rightarrow\ 4-\ln x=0\Rightarrow\ln x=4\Rightarrow\ x=e^4\\\text{OR}\ln x=\infty\Rightarrow\ x=0$

Hence, the vertical asymptotes of f(x) are:

$x=0\text{ and }x=e^4$.