\(27^x=3^{x+2}\)
\(\Rightarrow3^{3x}=3^{x+2}\)
\(\Rightarrow3^{3x}-3^{x+2}=0\)
\(\Rightarrow3^x.\left(3^{2x}-3^2\right)=0\)
\(\Rightarrow3^x.\left(3^{2x}-9\right)=0\)
Vì \(3^x>0\) \(\forall x.\)
\(\Rightarrow3^{2x}-9=0\)
\(\Rightarrow3^{2x}=0+9\)
\(\Rightarrow3^{2x}=9\)
\(\Rightarrow3^{2x}=3^2\)
\(\Rightarrow2x=2\)
\(\Rightarrow x=2:2\)
\(\Rightarrow x=1\)
Vậy \(x=1.\)
Chúc bạn học tốt!
Ta có: \(27^x=3^{x+2}\Leftrightarrow\left(3^3\right)^x=3^{x+2}\)
\(\Leftrightarrow3^{3x}=3^{x+2}\Leftrightarrow3x=x+2\Leftrightarrow3x-x-2=0\Leftrightarrow2x-2=0\Leftrightarrow2\left(x-1\right)=0\)
Vì 2>0 nên
x-1=0⇒x=1
Vậy: x=1
