Chapter 7.6, Problem 31PPE

To determine

Tosolve:The given equation.

Answer to Problem 31PPE

The solutions of equation $x+3=3^x$ are $x=-2.961$ and $x=1.335$ .

Explanation of Solution

Given information:

The given equation is $x+3=3^x$

Method used:

Let $y_1$ and $y_2$ be the function corresponding to Left Hand Side and Right hand side of the given equation, then the point of intersection of graphs of $y_1$ and $y_2$ is the solution of given equation.

Graph:

The given equation is $x+3=3^x$ .

Let $y_1=x+3$ and $y_2=3^x$ . The graphs of functions $y_1\left(x\right)=x+3$ and $y_2\left(x\right)=3^x$ are shown in Figure-1 here.

  

We see that the graphs of functions $y_1\left(x\right)=x+3$ and $y_2\left(x\right)=3^x$ coincide at points $A\left(-2.961,0.039\right)$ and $B\left(1.335,4.335\right)$ . That shows $x+3=3^x$ at $x=-2.961$ and $x=1.335$ .

Hence, $x=-2.961$ and $x=1.335$ are the solutions of equation $x+3=3^x$ .

Conclusion:

The solutions of equation $x+3=3^x$ are $x=-2.961$ and $x=1.335$ .