La solución del sistema de ecuaciones exponenciales : 3 ^ x - 1 - 2 ^ y = 11?

La solución del sistema de ecuaciones exponenciales planteada es : y = <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bln%288%2F5%29%20%7D%7Bln%282%29%7D" />x = <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bln%2811%2B2%5E%7B%5Cfrac%7Bln%288%2F5%29%20%7D%7Bln%282%29%7D%7D%29%7D%7Bln%283%29%7D%2B1" />Dado, <img src="https://tex.z-dn.net/?f=3%5E%7Bx-1%7D-2%5E%7By%7D%3D11" /> (1)<img src="https://tex.z-dn.net/?f=3%5E%7Bx%7D%2B2%5E%7By%2B1%7D%3D41" /> (2)Despejamos x de 1 ; <img src="https://tex.z-dn.net/?f=3%5E%7Bx-1%7D-2%5E%7By%7D%3D11" />sumar <img src="https://tex.z-dn.net/?f=2%5E%7By%7D" /> a ambos lados ; <img src="https://tex.z-dn.net/?f=3%5E%7Bx-1%7D-2%5E%7By%7D%2B2%5E%7By%7D%3D11%2B2%5E%7By%7D" /><img src="https://tex.z-dn.net/?f=3%5E%7Bx-1%7D%3D11%2B2%5E%7By%7D" />Por propiedad de logaritmo natural ; Si f(x) = g(x), entonces ln(f(x)) = ln (g(x))<img src="https://tex.z-dn.net/?f=ln%283%5E%7Bx-1%7D%29%3Dln%2811%2B2%5E%7By%7D%29" />Aplicando la propiedad : <img src="https://tex.z-dn.net/?f=log_%7Ba%7D%28x%5E%7Bb%7D%29%20%20%3D%20b.log_%7Ba%7D%28x%29" />[img = 10][img = 11]Dividimos ambos lados entre ln(3) ; [img = 12]x - 1 = [img = 13]Despejamos x ; x = [img = 14]Sustituimos x en 2 ; [img = 15] Restamos [img = 16] a ambos lados ; [img = 17] [img = 18] Aplicando la propiedad : [img = 19] [img = 20] Aplicando la propiedad : [img = 21][img = 22] Desarrollar : [img = 23] = [img = 24] = [img = 25]Aplicamos propiedades de logaritmos : [img = 26] = [img = 27] = [img = 28]Sumamos [img = 29] a ambos lados ; = [img = 30] = [img = 31] = [img = 32] = [img = 33] = [img = 34] = [img = 35] = [img = 36] = [img = 37] = [img = 38][img = 39]y = [img = 40]Sustituyo y en x ; x = [img = 41].