Question

Me ajudem a resolver essa equação exponencial:a) 6^3x=1 ,
b)4^x=1/16 ,
c) 100^x-4=1000^x
d)125^×-1=5^x+7,
e)(0,0001)^×=10^8-5x

Answer 1

a)6^3x  = 1 
6^3x = 6^0
3x = 0
x = 0/3
x = 0
b)4^4 = 1/16
4^x = 1/4²
4^x = 4^-2
x = - 2
c)100^x - 4 = 1000^x
(10²)x - 4 = (10³)^x
10^2x - 8 = 10^3 x
2x - 8 = 3 x
-8 = 3 x - 2 x
-8 = x
x = - 8
d)125^x - 1 = 5 ^x + 7
(5³)^x - 1   = 5^x + 7
3(x - 1 ) = x + 7
3x - 3 = x + 7
3x - x = 7 + 3
2 x = 10
x = 10/2
x = 5
e)0,0001^x = 10^8 - 5 x
10^-4 x = 10^8 - 5 x
-4 x = 8 - 5 x
-4 x + 5 x = 8
x = 8