If \(2^x + 2^{x+2} = 80\), find x.
4
We are given \(2^x + 2^{x+2} = 80\).
Write \(2^{x+2} = 2^x \cdot 2^2 = 4 \cdot 2^x\), so the equation becomes \(2^x + 4\cdot 2^x = 80\).
This gives \(5 \cdot 2^x = 80\), so \(2^x = 16 = 2^4\).
Hence \(x = 4\).
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