proszę o pomoc.. logarytmy magik: a)log_x64 − 6log₄x+7=0 b)log²x(logx−1)+(logx+1)logx−1)=7 c)log²₂x−3(log₂x−1)/log₂x−1=1 d)log₃x−1/log₃x+2 = log₃x−3/log₃x+4 e)2(log₁/3² x−1) =log_1/3x−log³_1/3x f)log₅³x+log²₅x=3−log₅x g)2log₂x²−log₂²(−x)=4 h)log²_1/9(−x−3)=log_1/3(x²+6x+9)+3

bdziumzde5: log₄ 64 = 6log₄(x+7) log₄ 64 = log₄(x+7)⁶ 64 = (x+7)⁶ 2⁶ = (x+7)⁶

Janek191: a) log_x 64 − 6 log₄ x + 7 = 0 ; x > 0 i x ≠ 1 log_x 4³ − 6 log₄ x + 7 = 0

	6
3 logx 4 −		+ 7 = 0
	logx 4

t = log_x 4

	6
3 t −		+ 7 = 0 / * t
	t

3 t² + 7 t − 6 = 0 Δ = 7² − 4*3*(−6) = 49 + 72 = 121 √Δ = 11

	− 7 − 11		− 7 + 11		2
t =		= − 3 lub t =		=
	6		6		3

więc

	2
logx 4 = − 3 lub logx 4 =
	3

1		1		2
	= − 3		=
log4 x		log4 x		3

	1		3
log4 x = −		log4 x =
	3		2

	1
x = 4−13 =		lub x = 432 = 8
	3√4