Question

Resolva a equação exponencial:
2^3x + 2^3x+1 + 2^3x+2 + 2^3x+3 = 240​

Answer 1

${2}^{3x} + {2}^{3x + 1} + {2}^{3x + 2} + {2}^{3x + 3} = 240$

${2}^{3x} + {2}^{3x}.2 + {2}^{3x} . {2}^{2} + {2}^{3x}. {2}^{3} \\ = 240$

${2}^{3x}(1 + 2 + 4 + 8) = 240 \\ {2}^{3x}.15 = 240 \\ {2}^{3x} = \frac{240}{15} \\ {2}^{3x} = 16$

${2}^{3x} = {2}^{4} \\ 3x = 4 \\ x = \frac{4}{3}$