Question

Resolva as equações exponenciais

Answer 1

a)2^x=64
2^x=2^6
x=6

b)3^(x-2)=9
3^(x-2)=3^2
x-2=2
x=2+2
x=4

c)5^(x^2-2x)=125
5^(x^2-2x)=5^3
x^2 -2x=3
x^2-2x-3=0 equação do 2° grau, logo
x,=3
x,,=-1
s={-1 e 3}

d)10^(1-x)=10^-1
1-x=-1
-x=-1-1
x=2

e)2^(4x-x^2)=8
2^(4x-x^2)=2^3
4x-x^2=3
-x^2+4x-3=0 *(-1)
x^2-4x+3=0
x,=3 e x,,=1
s={1,3}

f) (10^x)^(x-1)=10^-6
x^2-x=6
x^2-x-6=0
x,=3
x,,=-2
s={-2,3}

g)3^(2-x)=1/27
3^(2-x)=3^-3
2-x=-3
x=5

h) 3^(x-5)=27^(1-x)
3^(x-5)=3^3(1-x)
x-5=3-3x
x+3x=3+5
4x=8
x=2