Question

Resuelve la ecuación exponencial:
$3^x+3^{x+1}+3^{x+2}=1053$

Answer 1

Respuesta:

x=4

Factorizamos:

${3}^{x} ( 1 + {3}^{1} + {3}^{2} ) = 1053$

${3}^{x} (13) = 1053$

${3}^{x} = 81$

$x = 4$

Answer 2

...

${3}^{x} + {3}^{x + 1} + {3}^{x + 2} = 1053 \\ {3}^{x} ( {3}^{0} + {3}^{1} + {3}^{2} ) = 1053 \\ {3}^{x} (1 + 3 + 9) = 1053 \\ {3}^{x} (13) = 1053 \\ {3}^{x} = 81 \\ {3}^{x} = {3}^{4} \\ x = 4$