Chapter 6.6, Problem 64E

To determine

To explain:

The solution of the following inequality equation by using the given graph:

  $4\ln \mathrm{x}+6>9$

Answer to Problem 64E

The solution of the inequality equation is $\left({\mathrm{e}}^{\frac{3}{4}},9\right)$ .

Explanation of Solution

Given information:

  

Calculation:

Given inequality is $4\ln \mathrm{x}+6>9$ ,

This inequality equation is formed by two equations as:

  $\begin{array}{l}\mathrm{y}=4\ln \mathrm{x}+6>9\mathrm{...}\left(1\right)\\ \mathrm{y}=9\mathrm{...}\left(2\right)\end{array}$

Now graph the given two equation as below,

  

From the above graph it is observed that the intersection point of the two given line equations is solution of the given equation $4\ln \mathrm{x}+6>9$ .

So, the solution of the equation is $4\ln \mathrm{x}+6>9$ is $\left(2.117,9\right)$

The solution $\left(2.117,9\right)$ is equals to the $\left({\mathrm{e}}^{\frac{3}{4}},9\right)$ .