Równania logarytmiczne Wiikuś: a)log₄√x+¹₂log₄(x+4)=⁵₄ b)log₄(x²−1)−¹₂log₄(x+4)²=1¹₂ c)log(x−5)²+log(x+6)²=2

Janek191:

	5
a) log4 √x + 0,5 log4 ( x + 4) =		; x > 0
	4

1		5
	log2 x0,5 + 0,5*0,5 log2 (x + 4) =
2		4

1		1		5
	log2 x +		log2 ( x + 4) =		/ * 4
4		4		4

log₂ x + log₂ ( x + 4) = 5 log₂ x*(x + 4) = log₂ 2⁵ x² + 4 x = 32 x² + 4 x − 32 = 0 Δ = 16 − 4*1*(−32) = 16 + 128 = 144 √Δ = 12

	− 4 − 12		− 4 + 12
x =		< 0 − odpada lub x =		= 4
	2		2

Odp. x = 4 ========

Janek191: c) log ( x − 5)² + log ( x + 6)² = 2 ; x > 5 log [ ( x − 5)²*( x + 6)²} = log 100 (x − 5)²*( x + 6)² = 100