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\(2^1.2^2.2^3.....2^x=1024\Rightarrow2^{1+2+3+...+x}=2^{10}\)
\(\Rightarrow1+2+3+...+x=1024\Rightarrow x=4\)
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\(\Leftrightarrow2^n.\left(2^{-1}+4\right)=9.2^5\)
\(\Leftrightarrow2^n.4,5=4,5.2^6\)
\(\Rightarrow2^n=2^6\)
\(\Rightarrow n=6\)
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\(\left(\frac{1}{3}+\frac{1}{6}\right).2^{x+4}-2^x=2^{13}-2^{10}\)
\(\frac{1}{2}.2^x.2^4-2^x=8192-1024\)
\(2^x.8-2^x=7168\)
\(2^x\left(8-1\right)=7168\)
\(2^x.7=7168\)
\(2^x=7168\div7\)
\(2^x=1024\)
\(2^x=2^{10}\)
\(\Rightarrow x=10\)
Vậy \(x=10\).
(1/3+1/6).2^x.2^4-2^x=8192-1024
(1/3+1/6).2^x.2^4-2^x=7168
1/2.2^x.2^4-2^x=7168
1/2.2^x.(2^4-1)=7168
1/2.2^x.(8-1)=7168
1/2.2^x.7=7168
1/2.2^x=7168:7
1/2.2^x=1024
2^x=1024:1/2
2^x=2048
2^x=2^11
x=11
vậy x=11