Question

Rezolvati in R ecuatia:log2 (2x2+7)=log2 (x2+8)

Answer 1

Explicație pas cu pas:

$log_{2}(2 {x}^{2} + 7) = log_{2}( {x}^{2} + 8)$

$2 {x}^{2} + 7 = {x}^{2} + 8 \\ 2 {x}^{2} - {x}^{2} + 7 - 8 = 0 \\ {x}^{2} - 1 = 0 \\ (x + 1)(x - 1) = 0 \\ x + 1 = 0 = > x = - 1 \\ x - 1 = 0 = > x = 1$

=> x ∈ {-1; 1}