Question

Rezolvati in multimea numerelor reale ecuatia
$3 ^{x + 1} = 9 ^{x}$

Answer 1

Răspuns

Explicație pas cu pas:

3ˣ⁺¹ = 9ˣ <=> 3·3ˣ = 3²ˣ  => 3²ˣ - 3·3ˣ = 0

3ˣ = t => t²-3t = 0 <=> t(t-3) = 0 => t₁ = 0 ; t₂ = 3

3ˣ = t₁ <=> 3ˣ = 0 => nu are solutii

3ˣ = t₂ <=> 3ˣ = 3 => x = 1

Answer 2

${3}^{x + 1} = {9}^{x} \\ \\ {3}^{x + 1} = { {(3}^{2} )}^{x} \\ \\ {3}^{x + 1} = {3}^{2x} \\ \\ x + 1 = 2x \\ \\ (x + 1) + ( - x) = 2x + ( - x) \\ \\ x + 1 - x = 2x - x \\ \\ x - x + 1 = x \\ \\ 1 = x \\ \\ x = 1$