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Chapter 3: Problem 51

Use the One-to-One Property to solve the equation for \(x\). $$e^{3 x+2}=e^{3}$$

Short Answer

Expert verified
The solution to the equation is \(x = 1/3\).

Step by step solution

01

Apply the One-to-One Property

By the One-to-One property of exponents, since \(e^{3x+2} = e^3\), we can write that \(3x + 2 = 3\).
02

Solve for \(x\)

Rearrange the equation \(3x + 2 = 3\) to solve for \(x\), by subtracting 2 from both sides, getting \(3x = 1\). Then divide both sides by 3 to isolate \(x\). The solution will therefore be \(x = 1/3\).

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