Question

Alguém poderia resolver essas equações exponenciais para mim? POR FAVOR, É URGENTE. :(

Answer 1

a)2^(x+3) = 2^(-3)
x+3 = -3
x=-6

b) 5^(3x+1) = 5²
3x+1=2
3x=1
x=1/3

c) 3^(4x-8) = 3^(3/4)
4x-8 = 3/4
16x - 32 = 3
16x = 35
x=35/16



d) 4^(x+1) = 4^(2/3)
           2
x+1 = 2
 2       3
3x+3 = 4
3x=1
x=1/3

e) 5^(x/2) . 5^(2x+2) = 5 (-1+x)
5^(5x+4) = 5^(-1+x)
        2
5x+4 = -2+2x
3x=-6
x=-2

f) (2/5)^(x+3) = (5/2)^(3x-3) . (2/5)^(2x-3)
(2/5)^(x+3) = (2/5)^(-3x+3).(2/5)^(2x-3)
(2/5)^(x+3) = (2/5)^(-x)
x+3=-x
2x=-3
x= -3/2

g) 2^(2/5) . 2^(2x/3)= 2^(-3x/2)
2^(6/15+10x/15) = 2^(-3x/2)
6+10x = -3x
  15         2
-45x = 12 + 20x
-65x=12
x = -12/65

h) 1/3^(x+1) = 3^(1/2):3²
1/3^(x+1) = 3^(-3/2)
1/3^(x+1) = (1/3)^(3/2)
x+1=3/2
2x+2=3
2x=1
x=1/2

i) 1/2^(3x/2 - 2/2) = 1/2^(-4x) . (1/2)^(x-4)
1/2^(3x/2 - 2/2)= 1/2^(-3x-4)
3x-2  =  -3x-4
   2
3x-2=-6x-8
9x = -6
x= -2/3

j) 3^(3x) . 3^(6x) = 3^(-x+1)
3^(9x) =  3^(-x+1)
9x = -x+1
10x = 1
x=1/10