Chapter 3.3, Problem 96E

To determine

To find: The graph of given two logarithmic function on same viewing window.

Explanation of Solution

Given information:

Two logarithmic function is given as −

  $y_1=\ln x-\ln (x-3)$ and

  $y_2=\ln \left(\frac{x}{x-3}\right)$

Calculation:

Given two logarithmic functions are −

  $y_1=\ln x-\ln (x-3)$ and

  $y_2=\ln \left(\frac{x}{x-3}\right)$

Plotting these graph on same viewing window using a graphing utility.

  

  

From above graph domain of the function $y_1=\ln x-\ln (x-3)$ is $\left(3,\infty \right)$ .

And domain of the function $y_2=\ln \left(\frac{x}{x-3}\right)$ is $\left(-\infty ,0\right)\cup \left(3,\infty \right)$ .

Both are correct as per definition of logarithm - the function $y={\log }_{a}x$ is defined as logarithmic function where $y$ is called exponent and $a$ as base. Also, $x>0,a>0\text{ and }a\ne 1$ .