\(2^{2x-1}+6.2^8=14.2^8\)
\(2^{2x}:2+1536=3584\)
\(4^x:2=3584-1536=2048\)
\(4^x=2048:2=1024\)
\(4^x=4^5\Rightarrow x=5\)
\(\Leftrightarrow2^{2x-1}+6.2^8=\frac{2^{2x}+3072}{2}\)
\(\Rightarrow\frac{2^{2x}+3072}{2}=2^9.7\)
\(\Leftrightarrow2^{2x-1}+1536=3584\)
<=>2x-1=2048
=>x=6