Solve: \(2^{3x-7} = 256\)

Solution

\[ 2^{3x-7} = 256 \]

\[ 256 = 2^8 \]

\[ \Rightarrow 2^{3x-7} = 2^8 \]

\[ \Rightarrow 3x – 7 = 8 \]

\[ \Rightarrow 3x = 15 \]

\[ \Rightarrow x = 5 \]

Final Answer:

\[ \boxed{x = 5} \]

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