Đáp án đúng: A
Giải chi tiết:\(\begin{array}{l}{3^{x + 1}}.15 + {3^{x + 1}}.12 = {3^{21}}\\\,\,\,\,\,{3^{x + 1}}.\left( {15 + 12} \right) = {3^{21}}\\\,\,\,\,\,\,\,\,\,{3^{x + 1}}.27 = {3^{21}}\\\,\,\,\,\,\,\,\,\,\,{3^{x + 1}}{.3^3} = {3^{21}}\\\,\,\,\,\,\,\,\,\,\,{3^{x + 1 + 3}}\,\,\, = {3^{21}}\\\,\,\,\,\,\,\,\,\,\,{3^{x + 4}}\,\,\,\,\,\, = {3^{21}}\\\,\,\,\,\,\,\,\,\,\,x + 4\,\,\,\, = 21\\\,\,\,\,\,\,\,\,\,\,x\,\,\,\,\,\,\,\,\,\,\,\, = 21 - 4\\\,\,\,\,\,\,\,\,\,\,x\,\,\,\,\,\,\,\,\,\,\,\, = 17\,\,\end{array}\)
Vậy \(x = 17\).
Chọn A.