Question

Rezolvati in multimea numerelor reale ecuatia:
$2^{1}$ + $2^{x+1}$ = 6

Answer 1

${2}^{1} + {2}^{x + 1} = 6 \\ \\ {2}^{x + 1} + 2 = 6 \\ \\ ( {2}^{x + 1} + 2) + ( - 6) = 6 + ( - 6) \\ \\ {2}^{x + 1} + 2 - 6 = 6 - 6 \\ \\ {2}^{x + 1} - 4 = 0 \\ \\ ( {2}^{x + 1} - 4) + 4 = 4 \\ \\ {2}^{x + 1} - 4 + 4 = 4 \\ \\ {2}^{x + 1} = 4 \\ \\ {2}^{x + 1} = {2}^{2} \\ \\ x + 1 = 2 \\ \\ (x + 1) + ( - 1) = 2 + ( - 1) \\ \\ x + 1 - 1 = 2 - 1 \\ \\ x = 1$