Question

rezolvati in multimea numerelor reale ecuatia log2 (x-6)= 6- log2 (x+6)

Answer 1

Răspuns:

Explicație pas cu pas:

log₂(x-6)= 6- log₂(x+6) <=>

conditii : x-6 > 0 ; x+6 > 0  => x > 6

log₂(x-6) + log₂(x+6) = log₂2⁶ <=>

log₂[(x-6)(x+6)] = log₂64  =>

(x-6)(x+6) = 64  <=>

x²-36 = 64  => x² = 64+36  =>

x² = 100 => x₁,₂ = ± 10  =>

Solutie : x = 10