Question

1) Resolva no conjunto dos números reais as equações:

a) 12 elevado a x = 1
b) 5 elevado a x = 1/125
c) 3 elevado a x = 1/9
d) 2 elevado a x = 1/1024
e) (1/27) elevado a x = 1/9

Answer 1

a) 12ˣ=1 => 12ˣ=12⁰ => x=0

b)5ˣ=1/125 => 5ˣ=125⁻¹ => 5ˣ=(5³)⁻¹ => 5ˣ=5⁻³ => x=-3

c)3ˣ=1/9 => 3ˣ=9⁻¹ => 3ˣ=(3²)⁻¹ => 3ˣ=3⁻² => x=-2

d)2ˣ=1/1024 => 2ˣ=1024⁻¹ => 2ˣ=(2¹⁰)⁻¹ => 2ˣ=2⁻¹⁰ => x=-10

e)(1/27)ˣ=1/9 => [(1/3)³]ˣ=(1/3)² => (1/3)³ˣ=(1/3)² => 3x=2 => x=3/2