Question

resolva as potencias:

a) 125^x=25

b) 8^x+4=32^x

c) 16^x+1=64

d) 16^0,75=2^x

Answer 1

a)
125^x=25
5^3x=5^2
3x=2
x=2/3

b)
8^(x+4)=32^x
2^3(x+4)=2^5x
3(x+4)=5x
3x+12=5x
3x-5x=-12
-2x=-12
2x=12
x=12÷2
x=6

c)
16^(x+1)=64
2^4(x+1)=2^6
4(x+1)=6
4x+4=6
4x=6-4
4x=2
x=2/4
x=1/2

d)
16^0,75=2^x
2^4(0,75)=2^x
4(0,75)=x
x=3