Chapter 7.6, Problem 5P

a.

To determine

To find:The solution of ${0.3}^x=5$

Answer to Problem 5P

The solution of equation ${0.3}^x=5$ is $x=-1.337$ .

Explanation of Solution

Given:

The given equation is ${0.3}^x=5$ .

Concept used:

For each side given equation two equations are formed and graphed. The point(s) of intersection of two curves is/are the solutions of given equations.

Calculations:

Let $y_1={0.3}^x$ and $y_2=5$ .

The graphs and point of intersection of curves $y_1={0.3}^x$ and $y_2=5$ are shown in Figure-1.

  

The curves intersect at points $\left(-1.337,5\right)$ where $y_1=y_2\Rightarrow {0.3}^x=5$ .

Hence, $x=-1.337$ is the solution of equation ${0.3}^x=5$ .

Conclusion:

The solution of equation ${0.3}^x=5$ is $x=-1.337$ .

b.

To determine

To find: The solution of ${1.25}^x=-2x$

Answer to Problem 5P

The solution of equation ${1.25}^x=-2x$ is $x=-0.452$ .

Explanation of Solution

Given:

The given equation is ${1.25}^x=-2x$ .

Concept used:

For each side given equation two equations are formed and graphed. The point(s) of intersection of two curves is/are the solutions of given equations.

Calculations:

Let $y_1={1.25}^x$ and $y_2=-2x$ .

The graphs and point of intersection of curves $y_1={1.25}^x$ and $y_2=-2x$ are shown in Figure-2.

  

The curves intersect at points $\left(-0.452,0.904\right)$ where $y_1=y_2\Rightarrow {1.25}^x=-2x$ .

Hence, $x=-0.452$ is the solution of equation ${1.25}^x=-2x$ .

Conclusion:

The solution of equation ${1.25}^x=-2x$ is $x=-0.452$ .

c.

To determine

To find: The solution of $-\left(2^x\right)=\frac{3}{4}x-4$

Answer to Problem 5P

The solution of equation $-\left(2^x\right)=\frac{3}{4}x-4$ is $x=1.517$ .

Explanation of Solution

Given:

The given equation is $-\left(2^x\right)=\frac{3}{4}x-4$ .

Concept used:

For each side given equation two equations are formed and graphed. The point(s) of intersection of two curves is/are the solutions of given equations.

Calculations:

Let $y_1=-\left(2^x\right)$ and $y_2=\frac{3}{4}x-4$ .

The graphs, and the point of intersection of curves $y_1=-\left(2^x\right)$ and $y_2=\frac{3}{4}x-4$ are shown in Figure-3.

  

The curves intersect at points $\left(1.517,-2.862\right)$ where $y_1=y_2\Rightarrow -\left(2^x\right)=\frac{3}{4}x-4$ .

Hence, $x=1.517$ is the solution of equation $-\left(2^x\right)=\frac{3}{4}x-4$ .

Conclusion:

The solution of equation $-\left(2^x\right)=\frac{3}{4}x-4$ is $x=1.517$ .