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Chapter 3: Problem 24

Use the One-to-One Property to solve the equation for \(x .\) $$2^{x-3}=16$$

Short Answer

Expert verified
The solution to the equation \(2^{x-3}=16\) is \(x = 7\).

Step by step solution

01

Express both sides of the equation in terms of the same base

The given equation is \(2^{x-3}=16\). 16 can be expressed as \(2^4\). So we write the equation as \(2^{x-3}=2^4\).
02

Use the One-to-One property of exponents

Using the one-to-one property of exponents, if \(b^p=b^q\), then \(p=q\). Thus, we can say that \(x-3=4\).
03

Solve for \(x\)

Solving for \(x\), we can add 3 to both sides of the equation to get \(x=4+3=7\).

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