Question

Resolva as seguintes Equações Exponenciais

a) $3^{x}=81$

b) $2^{x}=256$

c) $7^{x}=7$

d)$0,5^{x}= \frac{1}{32}$

e) $5^{x+2}=125$

f)$10^{3x}=100000$

g) $\frac{1}{5} ^{x}= \frac{1}{625}$

h)$0,5 ^{x}=2$

Answer 1

a) 3^{x} = 3^{4} --> x = 4

b) 2^{x} = 2^{8} --> x = 8

c) 7^{x} = 7^{1} --> x  = 1

d) 0,5 = 1/2, logo: $( \frac{1}{2}) ^{x} = ( \frac{1}{2}) ^{5}$, Daí x = 5

e) 125 = 5³, logo x + 2 = 3 --> x = 3 - 2 --> x = 1

f) 100000 = 10^{5}, 3x = 5 ---> x = 5/3

g) 625 = 5^{4}, logo (1/5)^{x} = (1/5)^{4}  --> x = 4

h) (1/2)^{x} = 2
2^{-x} = 2¹
-x = 1
x = -1

Answer 2

a)   ==> 3^x = 3^4 ==> x = 4

b)  ==> 2^x = 2^8 ==> x = 8

c)   ==> 7^x = 7^1 ==> X = 1

d) ==> 2^-X = 2^-5 ==> -x = - 5(-1) ==> x = 5

e)  ==> 5^(x+2) = 5^3==>x+2 = 3 ==>x = 3-2 ==> x =1

f)==> 10^3x = 10^5==>3x=5==> x=5/3

g)  ==>  (1/5)^x = (1/5)^4==> x = 4

h) ==> 2^-x = 2^1 ==> - x = 2(-1) ==> x = - 2