Question

Calcule o valor de x nas equações
a)(16^x)^x+1=1/2
b)4^x+2=8^x+3
c)(1/32)^x-2=(1/64)^x-5
d)(16^x+2)^3=2^11

Answer 1

a
(16^x)^x +1  = 1/2
[(2)^4]^x+1  = 1/2
( 2)^4x+4 = (1/2)^-1
( 2)^4x+4 =( 2) ¹
4x + 4 = 1
4x = 1 - 4
4x = -3
x = -3/4 ***

b
4^x+2 = 8^x+3
(2²)^x+2 = (2³)^x+3
(2)^2x+4 = (2)^3x+9
2x + 4 = 3x + 9
2x - 3x = 9 - 4
-x = 5
x = -5 ****
c
(1/32)^x -2 = ( 1/64)^x-5
[(1/2)^5]^x-2=[ (1/2)^6]^x-5
(1/2)^5x-10= (1/2)^6x-30
5x - 10 = 6x - 30
5x - 6x = -30 + 10
-x = -20
x = 20 ***
d
[( 16)^x+2]³= 2^11
[(2^4)^3x+6] = 2^11
( 2 )^12x+24 = 2^11
12x + 24 = 11
12x = 11 - 24
12x= -13
x = -13/12 ***