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Chapter 3: Problem 23

Use the One-to-One Property to solve the equation for \(x .\) $$3^{x+1}=27$$

Short Answer

Expert verified
The solution for the equation \(3^{x+1}=27\) is \(x = 2\).

Step by step solution

01

Understand the problem

The equation given is \(3^{x+1}=27\). To apply the the One-to-One Property of exponential functions, it's necessary to express \(27\) as \(3^m\). Note that \(27 = 3^3\).
02

Apply the One-to-One Property

Having the same base allows to setting the equations equal. This gives the following equation: \(3^{x+1}=3^3\). By the One-to-One Property, the exponents must be equal. Therefore the equation \(x+1 = 3\) can be written.
03

Solve for x

The equation can be further simplified to find the value of \(x\) by subtracting \(1\) from both sides of the equation. After subtraction, it can be found that \(x = 2\).

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