Đáp án:
Giải thích các bước giải:
\(\begin{array}{l}a)\,{3^x} + {3^{x + 1}} + {3^{x + 2}} = 1053\\\,\,\,\,\,\,{3^x} + {3.3^x} + {3^2}{.3^x} = 1053\\\,\,\,\,\,\,{3^x}.\left( {1 + 3 + 9} \right) = 1053\\\,\,\,\,\,\,{3^x}.13\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1053\\\,\,\,\,\,\,{3^x}\,\, = 1053:13\\\,\,\,\,\,\,{3^x} = 81\\\,\,\,\,\,\,{3^x} = {3^4}\\ \Rightarrow x = 4\\b)\,{5^x}{.5^{19}} = {5^{20}}{.5^{11}}\\ \Leftrightarrow {5^{x + 19}} = {5^{20 + 11}}\\ \Leftrightarrow {5^{x + 19}} = {5^{31}}\\ \Rightarrow x + 19 = 31\\ \Rightarrow x = 31 - 19\\ \Rightarrow x = 12\\c)\,{x^{2005}} = x\\ \Leftrightarrow {x^{2005}} = {x^1}\\ \Leftrightarrow x = 1\,\,\,\,\,hoac\,\,\,x = 0\end{array}\)
