Question

Please solve this question as soon as possible​

Answer 1

$9^{x+1}-244\cdot 3^x+27=0\\\\9^x\cdot 9-244\cdot 3^x+27=0\\\\(3^x)^2\cdot 9-244\cdot 3^x+27=0$

$\textsf {Let}\ 3^x=k.\ \textsf {Then,}$

$9k^2-244k+27=0\\\\9k^2-243k-k+27\\\\\\\implies\ k=\dfrac {243}{9}\quad;\quad k=\dfrac {1}{9}\\\\\\3^x=27\quad;\quad 3^x=\dfrac {1}{9}\\\\\\3^x=3^3\quad;\quad 3^x=3^{-2}\\\\\implies\ \large\boxed{x=3\quad;\quad x=-2}$