Question

solve. write your answer as an integer or a fraction in simplest form.
\\(\frac{1}{2} = 2^{2x - 2}\\)
\\(x = \boxed{}\\)

Explanation:

Step1: Rewrite \(\frac{1}{2}\) as a power of 2

We know that \(\frac{1}{2} = 2^{-1}\), so the equation becomes \(2^{-1}=2^{2x - 2}\).

Step2: Set the exponents equal

Since the bases are the same (both are 2), we can set the exponents equal to each other: \(-1 = 2x-2\).

Step3: Solve for \(x\)

Add 2 to both sides of the equation: \(-1 + 2=2x-2 + 2\), which simplifies to \(1 = 2x\). Then divide both sides by 2: \(x=\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)