Question

Resolva, em R as seguintes equações exponenciais. a) 8^x= 16 b)27^x= 27 c) 4^x= 32 d) 25^x =625 e) 9^x = 1/27 f) 4^x = 1/2 g)1/25^x = 125 H)1/4^x = 1/8

Answer 1

a) 8^x= 16 ==> (2^3)^x=2^4==>2^3x=2^4==> 3x=4 ==> x = 4/3
b)27^x= 27==> (3^3)^x=3^3==>3^3x=3^3==> 3x=3 ==> x = 1 
c) 4^x= 32 ==> (2^2)^x=2^5==>2^2x=2^5==> 2x=5 ==> x = 5/2
d) 25^x =625 ==> (5^2)^x=5^4==>5^2x=5^4==> 2x=4 ==> x = 2
e) 9^x = 1/27 ==> (3^2)^x=3^-3==>3^3x=3^-1==> 3x= - 1 ==> x = - 1/3
f) 4^x = 1/2 ==>(2^2)^x=2^-1==>2^2x=2^-1==> 2x= - 1 ==> x = - 1/2
g)1/25^x = 125 ==>(5^-2)^x=5^3==>5^-2x=5^3==> -2x= 3 ==> x = - 3/2
H)1/4^x = 1/8==>(2^-2)^x=2^-3==>2^-2x=2^-3==> -2x= - 3 ==> x = 3/2

Answer 2

EQUAÇÕES EXPONENCIAIS 1° TIPO

a) 8^x=16 

fatorando o 8 e 16, temos: 2^3(x)=2^4 eliminando as bases e conservando os expoentes, temos: 3x=4 ==> x=4/3

b) 27^x=27 ==>27^x=27¹ ==> x=1

c) 4^x=32 ==> 2^2(x)=2^5 ==> 2x=5 ==> x=5/2

d) 25^x=625 ==> 25^x=5^4 ==> x=4

e) 9^x=1/27 ==> 3^3(x)=1/2^3 ==> 3^3x=2^-3 ==> 3x= -3 ==> x= -1

f) 4^x=1/2 ==> 2^2(x)= 1/2^1 ==> 2^2x=2^-1 ==> 2x= -1 ==> x= -1/2

g) 1/25^x=125 ==> 1/5^2(x)= 5^3 ==> 5^-2x=5^3 ==> -2x=3 ==> x= -3/2

h) 1/4^x=1/8 ==> 1/2^2(x)=1/2^3 ==> 2^-2x=2^-3 ==> -2x=-3 ==> x= 3/2