Chapter 3.4, Problem 111E

a.

To determine

To complete: the table,

  

Using the function $\ln (2x)=2.4$ .

Answer to Problem 111E

  $(2,1.386),(3,1.792),(4,2.079),(5,2.302),(6,2.484)$

Explanation of Solution

Given information :

Given function $\ln (2x)=2.4$ .

  $\begin{array}{l}\ln (2x)=2.4\\ x=2\Rightarrow \ln (2x)=\ln (4)=1.386\\ x=3\Rightarrow \ln (2x)=\ln (6)=1.792\\ x=4\Rightarrow \ln (2x)=\ln (8)=2.079\\ x=5\Rightarrow \ln (2x)=\ln (10)=2.302\\ x=6\Rightarrow \ln (2x)=\ln (12)=2.484\end{array}$

So the points are $(2,1.386),(3,1.792),(4,2.079),(5,2.302),(6,2.484)$ upto three decimal places.

b.

To determine

To find: the graph using the points $(2,1.386),(3,1.792),(4,2.079),(5,2.302),(6,2.484)$ .

Explanation of Solution

Given information:

Obtained data $(2,1.386),(3,1.792),(4,2.079),(5,2.302),(6,2.484)$

Graph:

The intersecting point is $(5.511,2.40)$up to three decimal places.

  

So the solution is $x\approx 5.511$ .

c.

To determine

To solve: the equation $\ln (2x)=2.4$ algebraically.

Answer to Problem 111E

  $x=5.511$ (Correct up to three decimal places)

Explanation of Solution

Given information :

Given equation $\ln (2x)=2.4$ .

Now,

  $\begin{array}{l}\ln (2x)=2.4\\ \Rightarrow 2x=e^{2.4}\\ \Rightarrow x=\frac{e^{2.4}}{2}=5.511\end{array}$

Correct up to three decimal places.