\(5^x-2-3^2=2^4-\left(2^8x2^4-2^{10}x2^2\right)\)
\(5^x-2-3^2=2^4-\left(2^{8+4}-2^{10+2}\right)\)
\(5^x-2-3^2=2^4-\left(2^{12}-2^{12}\right)\)
\(5^x-2-3^2=2^4-0\)
\(5^x-2-3^2=2^4\)
\(5^x-2-9=16\)
\(5^x-2=16+9\)
\(5^x-2=25\)
\(5^x=25+2\)
\(5^x=27\)
Bởi vì 27 không phân tích được 1 số có số mũ là 2
\(\Rightarrow\) Không tồn tại x
\(5^{x-2}-9=16-\left(256.16-1024.4\right)\)
\(\Rightarrow5^{x-2}-9=16-\left(4096-4096\right)\)
\(\Rightarrow5^{x-2}-9=16-0\)
\(\Rightarrow5^{x-2}-9=16\)
\(\Rightarrow5^{x-2}=25\)
\(\Rightarrow x-2=25:5\)
\(\Rightarrow x-2=3\)
\(\Rightarrow x=5\)
\(5^{x-2}-3^2=2^4-\left(2^8\cdot2^4-2^{10}\cdot2^2\right)\)
\(\Rightarrow5^{x-2}-3^2=2^4-\left(2^{12}-2^{12}\right)\)
\(\Rightarrow5^{x-2}-9=16-0\)
\(\Rightarrow5^{x-2}=16+9\)
\(\Rightarrow5^{x-2}=25\)
\(\Rightarrow5^{x-2}=5^2\)
\(\Rightarrow x-2=2\)
\(\Rightarrow x=2+2\)
\(\Rightarrow x=4\)
Vậy: x=4
