log₂(x+14)+log₂(x+2)=6
x>-14
x>-2
x∈(-2 , +∞)
Odp.
Pomodlem daj naj :)
log 2 [ x + 14] + log 2 [ x + 2 ] = 6
Założenia:
x + 14 > 0 i x + 2 > 0
czyli x > - 14 i x > - 2
x > - 2
======
Mamy
log 2 [ ( x +14)*( x + 2) ] = log 2 [ 2^ 6]
( x + 14)*( x + 2) = 64
x^2 + 16 x + 28 - 64 = 0
x^2 + 16 x - 36 = 0
--------------------------
delta = 16^2 - 4*1*( -36) = 256 + 144 = 400
p Idelty) = 20
x = [ - 16 + 20]/2 = 4/2 = 2 > - 2
lub
x = [ -16 - 20 ]/2 = - 36/2 = - 18 < - 2 odpada
Odp. x = 2
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x>-14
x>-2
x∈(-2 , +∞)
Odp.
Pomodlem daj naj :)
log 2 [ x + 14] + log 2 [ x + 2 ] = 6
Założenia:
x + 14 > 0 i x + 2 > 0
czyli x > - 14 i x > - 2
x > - 2
======
Mamy
log 2 [ ( x +14)*( x + 2) ] = log 2 [ 2^ 6]
( x + 14)*( x + 2) = 64
x^2 + 16 x + 28 - 64 = 0
x^2 + 16 x - 36 = 0
--------------------------
delta = 16^2 - 4*1*( -36) = 256 + 144 = 400
p Idelty) = 20
x = [ - 16 + 20]/2 = 4/2 = 2 > - 2
lub
x = [ -16 - 20 ]/2 = - 36/2 = - 18 < - 2 odpada
Odp. x = 2
==============