Question

05. Resuelva la ecuación:
2^×+3+2^×+1 - 2^×+2 - 2^× = 50^×​

Answer 1

Explicación paso a paso:

${2}^{x + 3} + {2}^{x + 1} - {2}^{x + 2} - {2}^{x} = {50}^{x} \\ {2}^{x} . {2}^{3} + {2}^{x} . {2}^{1} - {2}^{x} . {2}^{2} - {2}^{x} = {50}^{x} \\ {2}^{x} ( {2}^{3} + 2 - {2}^{2} - 1) = {50}^{x} \\ {2}^{x} (8 + 2 - 4 - 1) = (2 \times 25 {)}^{x} \\ {2}^{x} (5) = {2}^{x} \times {5}^{2x} \\ 5 = {5}^{2x} \\ 2x = 1 \\ x = \frac{1}{2}$