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Chapter 12: Problem 129

Use your graphing utility to graph each side of the equation in the same viewing rectangle. Then use the \(x\) -coordinate of the intersection point to find the equation's solution set. Verify this value by direct substitution into the equation. $$3^{x}=2 x+3$$

Short Answer

Expert verified
The solution to the equation \(3^x = 2x + 3\) is the x-coordinate of the point where the graphs of the functions \(y = 3^x\) and \(y = 2x + 3\) intersect. This value is finally confirmed by directly substituting it into the initial equation.

Step by step solution

01

Graph the Functions

Start by graphing each function, \(y = 3^x\) and \(y = 2x + 3\), on the same cartesian plane using a graphic calculator or utility.
02

Find the Intersection Point

After the graphs have been plotted, they will intersect at certain points. Find the x-coordinate of the point where the graphs intersect.
03

Direct Substitution Verification

After obtaining the x-coordinate of the intersection point, substitute this value into both sides of the equation \(3^x = 2x + 3\). If the left side equals the right side, the solution is correct. This process is known as direct substitution verification.

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