解方程：\( x^x =3^{x+243} \)
\(x^x=3^x\cdot3^{243} \)
\((\frac{x}{3})^x =3^{243} \)
\([(\frac{x}{3})^x]^{\frac{1}{3}} =[3^{243}]^{\frac{1}{3}} \)
\((\frac{x}{3})^{\frac{x}{3}} =3^{81} \)
\((\frac{x}{3})^{\frac{x}{3}} =3^{3\cdot27} \)
\((\frac{x}{3})^{\frac{x}{3}} =27^{27} \)
\(\frac{x}{3} = 27\)
\(x = 81\)