Question

Va rog rezolvati cateva a, b, c daca nu vreti pe toate ca sa inteleg cum se face

Answer 1

E3. a) (4/9)^x+1 * ( 27/8)^x = 2/3
(2/3)^2x+2 * (3/2)^3x = (2/3)^1
(2/3)^2x+2 * ( 2/3)^-3x = (2/3)^1
(2/3)^-x+2 = (2/3)^1
-x+2=1
-x=1-2
-x=-1
x=1 


b) (3/11)^3x-10 = (11/3)^7x-10
(3/11)^3x-10 = (3/11)^-(7x+10)
(3/11)^3x-10 = (3/11)^-7x+10
3x-10 = -7x+10
3x+7x = 10+10
10x = 20
x = 2

c) (0,25)^3 = 256/2^x+5
2^-6+2x = 2^3-x
-6+2x = x-3
2x+x = 3+6
3x = 9
x = 3


d) (0,4)^x-4 = (6.25)^4x-7
(2/5)^x-4 = (2/5)^-8x+14
x-4=-8x+14
x+8x = 14+4
9x=18
x=2

e) 32^x+6/x-6 = 0,25*128^x+18/x-2
5x+30/x-6 = 5x+130/x-2
(5x+30)(x-2)=(5x+130)(x-6)
5x^2 - 10x +30x - 60 = 5x^2 -30x+130x-780
20x-60=100x-780
20x-100x = -780+60
-80x = -720
x=9


f) (3/5)^x * ( 25/27)^x = 125/729
(3/5 * 25/27 ) ^x = (5/9)^3
(5/9)^x = (5/9)^3
x=3