(√81 ^ x + 2 ?

Tarea(√81 ^ x + 2 .

27 ^ 2x + 1) / 3√243 ^ 2x = 3 ^ 5x + 5Respuesta : x = 0Explicación paso a paso : Hola!

Se va factorizando hasta que quede la misma base y se aplica las propiedades correspondientes de potencia<img src="https://tex.z-dn.net/?f=%5Cdfrac%7B%28%5Csqrt%7B81%7D%5E%7Bx%2B2%7D.27%5E%7B2x%2B1%7D%29%7D%7B%5Csqrt%5B3%5D%7B243%7D%5E%7B2x%7D%7D%3D3%5E%7B5x%2B5%7D%5C%5C%5C%5CAhora%5C%20pasamos%5C%20los%5C%20indices%5C%20a%20exponentes%5C%20fraccionarios%5C%5C%5C%5C%5Csqrt%7Ba%7D%3Da%5E%5Cfrac%7Bpotencia%7D%7Bindice%7D%2C%20entonces%5C%5C%5C%5C%5C%5C%20%5Cdfrac%7B%2881%5E%7Bx%2B2%7D%29%5E%5Cfrac%7B1%7D%7B2%7D%5C%20.%5C%2027%5E%7B2x%2B1%7D%7D%7B%28243%5E%7B2x%7D%29%5E%5Cfrac%7B1%7D%7B3%7D%7D%3D%203x%5E%7B5x%2B5%7D%5C%5C%5C%5CAhora%5C%20escribimos%5C%20las%5C%20bases%5C%20en%20%5C%20funcion%5C%20de%5C%203%5C%5C%5C%5C%5Cdfrac%7B%5Cleft%28%283%5E4%29%5E%7B%28x%2B2%29%5Cright%29%5E%5Cfrac%7B1%7D%7B2%7D%7D.%5C%20%283%29%5E%7B3%282x%2B1%29%7D%7D%7B%5Cleft%28%283%5E5%29%5E%7B2x%7D%5Cright%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%7D%3D3%5E%7B5x%2B5%7D" />

<img src="https://tex.z-dn.net/?f=Multiplicamos%5C%20las%20%5C%20potencias%5C%20de%5C%20potencias%5C%5C%5C%5C%5Cdfrac%7B%283%29%5E%7B4.%28x%2B2%29.%5E%5Cfrac%7B1%7D%7B2%7D%7D.%5C%20%283%29%5E%7B3%282x%2B1%29%7D%7D%7B%283%29%5E%7B5.2x%7D.%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%7D%3D3%5E%7B5x%2B5%7D%20%5C%5C%5C%5C%5C%5C%5Cdfrac%7B%283%29%5E%7B2x%2B2%7D.%5C%20%283%29%5E%7B6x%2B3%7D%7D%7B%283%29%5E%7B%5Cfrac%7B10%7D%7B3%7Dx%7D%7D%3D3%5E%7B5x%2B5%7D%20%5C%5C%5C%5C%5C%5CAplicamos%20%5C%20las%20%5C%20propiedades%5C%20de%5C%20potencia%5C%5C%5C%5C%2B%20Multiplicacion%5C%20de%5C%20igual%5C%20base%5C%20se%20%5C%20suman%5C%20los%5C%20exponentes%5C%5C%5C%5C%2BDivision%5C%20de%5C%20igual%5C%20base%5C%20se%5C%20restan%5C%20los%5C%20exponentes%5C%5C%5C%5C3%5E%7B%282x%2B2%29%2B%286x%2B3%29-%28%5Cfrac%7B10%7D%7B3%7Dx%29%7D%3D3%5E%7B5x%2B5%7D" />

<img src="https://tex.z-dn.net/?f=Se%20%5C%20cancelan%5C%20las%5C%20bases%5C%5C%5C%5C%20%7B%282x%2B2%29%2B%286x%2B3%29-%28%5Cfrac%7B10%7D%7B3%7Dx%29%7D%3D%7B5x%2B5%7D%5C%5C%5C%5CResolvemos%5C%5C%5C%5C2x%2B2%2B6x%2B3-%5Cfrac%7B10%7D%7B3%7Dx%3D%205x%2B5%5C%5C%5C%5C%20Juntamos%5C%20los%5C%20terminos%20%5C%20semejantes%5C%5C%5C%5C2x%2B6x-%5Cfrac%7B10%7D%7B3%7Dx-5x%3D5-2-3%5C%5C%5C%5C2x%2B6x-%5Cfrac%7B10%7D%7B3%7Dx-5x%3D%200%5C%5C%5C%5C3x-%5Cfrac%7B10%7D%7B3%7Dx%3D%200%5C%5C%5C%5C%5Cfrac%7B9x-10x%7D%7B3%7D%3D%200%5C%5C%5C%5C9x-10x%3D0%5C%5C%5C%5C-x%3D0%5Cto%20%5Cboxed%7Bx%3D0%7D" /><img src="https://tex.z-dn.net/?f=Verificaci%5C%27on%3A%5C%5C%5C%5C%20%5Cdfrac%7B%5Csqrt%7B81%5E%7Bx%2B2%7D%7D%20%5C%20.27%5E%7B2x%2B1%7D%7D%7B%5Csqrt%5B3%5D%7B243%5E2%5Ex%7D%7D%3D3%5E%7B5x%2B5%7D%20%5Cqquad%5Cqquad%20x%3D0%5C%5C%5C%5C%5C%5C%20%5Cdfrac%7B%5Csqrt%7B81%5E%7B0%2B2%7D%7D%5C%20.27%5E%7B2.0%2B1%7D%7D%7B%5Csqrt%5B3%5D%7B243%5E2.%5E0%7D%7D%3D3%5E%7B5.0%2B5%7D%20%5C%5C%5C%5C%5C%5C%20%5Cdfrac%7B%5Csqrt%7B3%5E4%7D%5E%7B2%7D%5C%20.3%5E3%7D%7B%5Csqrt%5B3%5D%7B243%5E0%7D%7D%3D3%5E%7B5%7D%5C%5C%5C%5C%5C%5C%20%5Cdfrac%7B3%5E4%5C%20.3%5E3%7D%7B%5Csqrt%5B3%5D%7B1%7D%7D%3D3%5E%7B5%7D%5C%5C%5C%5C%20%5Cboxed%7B3%5E5%3D3%5E5%7D" />Espero que te sirva, salu2!