Question

Rezolvați in R ecuația 2la puterea x+1 + 2 la puterea x+3=40
${2}^{x + 1} + {2}^{x + 3} = 40$

Answer 1

${2}^{x + 1} + {2}^{x + 3} = 40$

${2}^{x} \times 2 + {2}^{x} \times {2}^{3} = 40$

${2}^{x} (2 + {2}^{3} ) = 40$

${2}^{x} (2 + 8) = 40$

${2}^{x} \times 10 = 40 \: | \div 10$

${2}^{x} = 4 = > x = 2\:\in\:\mathbb{R}$