Question

Resolva as equações exponenciais
a.4^(x-1)=1/2
b.4^x=0,25
c.125^x=0,04
d.81^(4-31)=9^(5-x)
e.8^(x-9)=(1/2)^(x+1)
Alguem me ajuda por favor !!

Answer 1

a)
4^(x-1)=1/2
2²^(x-1)=1/2
1/2^(-2)^(x-1)=1/2
1/2^(-2x+2)=1/2¹
-2x+2=1
x= 1/2

b)
4^x=0,25
4^x=1/4
1/4^(-1)^(x)=1/4¹
-x=1
x= -1

c)
125^x=0,04
125^x=4/100
125^x=1/25
5³^x=1/5²
1/5^(-3x)=1/5²
-3x=2
x= -2/3

d)
81^(4-31)=9^(5-x)
9²^(-27)=9^(5-x)
-54=5-x
-x=-59
x=59

e)
8^(x-9)=(1/2)^(x+1)
2³^(x-9)=1/2^(x+1)
1/2^(-3)^(x-9)=1/2^(x+1)
-3x+27=x+1
4x=26
x=13/2