$$3^{2x}-10.3^{x}+27=0.$$
$x=\frac{1}{3}\left(2\ln(18)+3\ln(\left(-\frac{1}{72}\right)\left(\left(-1\right)\left(-243+47049^{\frac{1}{2}}\right)^{\frac{1}{3}}+i\left(-243+47049^{\frac{1}{2}}\right)^{\frac{1}{3}}\times 3^{\frac{1}{2}}+2\left(-243+\left(-1\right)\times 47049^{\frac{1}{2}}\right)^{\frac{1}{3}}\right)\left(\left(-i\right)\times 3^{\frac{1}{2}}+1\right))+6i\pi n_{1}\right)\ln(3)^{-1}\text{, }n_{1}\in \mathrm{Z}$
$x=\frac{1}{3}\left(3\ln(\left(-243+47049^{\frac{1}{2}}\right)^{\frac{1}{3}}+\left(-243+\left(-1\right)\times 47049^{\frac{1}{2}}\right)^{\frac{1}{3}})+\left(-1\right)\ln(18)+6i\pi n_{2}\right)\ln(3)^{-1}\text{, }n_{2}\in \mathrm{Z}$
$x=\frac{1}{3}\left(2\ln(18)+3\ln(\left(-\frac{1}{72}\right)\left(\left(-1\right)\left(-243+47049^{\frac{1}{2}}\right)^{\frac{1}{3}}+\left(-i\right)\left(-243+47049^{\frac{1}{2}}\right)^{\frac{1}{3}}\times 3^{\frac{1}{2}}+2\left(-243+\left(-1\right)\times 47049^{\frac{1}{2}}\right)^{\frac{1}{3}}\right)\left(i\times 3^{\frac{1}{2}}+1\right))+6i\pi n_{3}\right)\ln(3)^{-1}\text{, }n_{3}\in \mathrm{Z}$