Bài 3:
\(\Rightarrow2C=8+2^3+2^4+...+2^{2022}\\ \Rightarrow2C-C=8+2^3+2^4+...+2^{2022}-4-2^2-...-2^{2021}\\ \Rightarrow C=2^{2022}+8-4-2^2=2^{2022}\left(đpcm\right)\)
Bài 4:
\(\Rightarrow2^y\left(2^{x-y}-1\right)=2^7\\ \Rightarrow2^{x-y}-1=2^{7-y}\)
Vì \(2^{x-y}-1\) lẻ nên \(2^{7-y}=1=2^0\Rightarrow7-y=0\Rightarrow y=7\)
\(\Rightarrow2^x-2^7=128\\ \Rightarrow2^x=256\\ \Rightarrow x=8\)
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