Chapter 4.4, Problem 4QR

To determine

To calculate:The simplification of the given expression.

Answer to Problem 4QR

The simplified expression is $\ln \left(x-2\right)$ .

Explanation of Solution

Given information:The expression is given as,

  $\ln \left(x^2-4\right)-\ln \left(x+2\right)$

Formula used:

  $\ln a-\ln b=\ln \left(\frac{a}{b}\right)$ ........ (1)

Calculation:Using the equation given in equation (1),

  $\begin{array}{l}\ln \left(x^2-4\right)-\ln \left(x+2\right)=\ln \left(\frac{x^2-4}{x+2}\right)\\ \ln \left(x^2-4\right)-\ln \left(x+2\right)=\ln \left(\frac{\left(x-2\right)\left(x+2\right)}{x+2}\right)\\ \ln \left(x^2-4\right)-\ln \left(x+2\right)=\ln \left(x-2\right)\end{array}$

The given value is converted as $\ln \left(x-2\right)$ .