Rozwiaz rownanie rown: a)5^x = 6^x+1 b)11^x−3 = 13^3−x c) 7^x+1 = 3^2x−2 d) 3^2x = 2^x * 4^x−1 Ktos by mogl mi napisać krok po kroku jak rozwiazac te rownania?

yht: a) 5^x = 6^x * 6¹ 5^x = 6 * 6^x ||:6^x

5x
	= 6
6x

	5
(		)x = 6
	6

x = log_5/66 b) 11^x−3 = 13^3−x

	13
11x−3 = (		)3−x
	1

	1
11x−3 = {		)x−3
	13

	1
{		)x−3 = 11x−3 ||:11x−3
	13

(1/13)x−3
	= 1
11x−3

1/13
	)x−3 = 1
11

	1
{		)x−3 = 1
	143

x−3 = log_1/1431 x−3 = 0 x = 3 c) 3^2x = 2^x * 4^x−1 3^2x = 2^x * (2²)^x−1 3^2x = 2^x * 2^2*(x−1) 3^2x = 2^x * 2^2x−2 3^2x = 2^x * 2^2x * 2⁻²

	1
32x = 2x+2x *
	4

	1
32x = 23x *
	4

	1
(32)x = (23)x *
	4

	1
9x = 8x *		||:(8x)
	4

9x		1
	=
8x		4

	9		1
(		)x =
	8		4

x = log_9/81/4

yht: brakujący przykład: 7^x+1 = 3^2x−2 7^x * 7¹ = 3^2x * 3⁻²

	1
7 * 7x = (32)x *
	9

	1
7 * 7x = 9x *		|*9
	9

63 * 7^x = 9^x ||:7^x

	9x
63 =
	7x

	9
63 = (		)x
	7

	9
(		)x = 63
	7

x = log_9/763