Question

Exercícios :
3) Resolva as equações exponenciais :)
a) 5^x = 125
e) 2^x+3 =64
b) 3^x=3 =27
f) 2^x = 1/32
c) 72^x-4 = 1
g)22^x+4=1/16
d) 32^x-5 = 3
h)52^x+1=1/125​

Answer 1

a) 5^x = 125

5^x = 5^3 ===> x=3

e) 2^x+3 =64

2^x+3 = 2^6 => x+3=6 => x= 3

b) 3^x=3 =27

3^x+3 = 3^3 => x+3=3 => x=0

f) 2^x = 1/32

2^x = 2^-5 ==> x= -5

c) 72^x-4 = 1

7^2x-4 = 7^0 => 2x-4=0 => 2x=4 => x=2

g)22^x+4=1/16

2^2x+4 = 2^-4 => 2x+4=-4 => 2x= -8 => x=-4

d) 32^x-5 = 3

3^2x-5 = 3^1 => 2x-5=1 => 2x=6 => x=3

h)52^x+1=1/125

5^2x+1 = 5^-3 => 2x+1=-3 => 2x=-4 => x= -2