rozwiaz rownanie ANIA: rozwiaz rownanie wykladnicze: a) 16^x+1+4²x+2⁴x= u(9)(8) b) 2*16^x+4=9*4^x c) 3^x+2−2*3^x=63

Janek191: Cz taki jest zapis w a)

	9
16x + 1 + 42x + 24x =		?
	8

ANIA: tak taki zapis zgadza sie

Janek191: b) 2* 16^x + 4 = 9*4^x 2*( 4²)^x + 4 = 9*4^x 2*4^2x + 4 = 9*4^x 2*( 4^x)² − 9*4^x+ 4 = 0 t = 4^x > 0 2 t² − 9 t + 4 = 0 Δ = (−9)² − 4*2*4 = 81 − 32 = 49 √Δ = 7

	9 − 7		1		9 + 7
t =		=		lub t =		= 4
	4		2		4

zatem

	1
4x =		lub 4x = 4
	2

	1
x = −		lub x = 1
	2

=====================

Janek191:

	9
a) 16 x + 1 + 42x + 24x =
	8

	9
(24) x + 1 + (22)2x + 24x =
	8

	9
24x + 4 + 24x + 24x =
	8

	9
24* 24x + 2*24x =
	8

	9
16*24x + 2*24x =
	8

	9
18*24x =		/ : 18
	8

	9
24x =
	8*18

	1
24x =		= 2−4
	16

4x = − 4 x = − 1 =====

Janek191: c) 3^{x + 2} − 2*3^x = 63 3^x * 3² − 2*3^x = 63 9*3^x − 2*3^x = 63 7*3^x = 63 / : 7 3^x = 9 = 3² więc x = 2 =====