Question

determine o valor das expressões a seguir utilizando o artifício de elevar base e antilogaritmo a um expoente comum:
a)8log25=
b)5log252=

Answer 1

Resposta:

a)  

8^(log₂ 5)=x

x =  8^(log₂ 5)

log₂ x = log₂ ( 8^(log₂ 5))

log₂ x = (log₂ 5) * log₂ 8

log₂ x =( log₂ 5) * log₂ 2³

log₂ x = (log₂ 5) * 3* log₂ 2

log₂ x = (log₂ 5) * 3* 1

log₂ x =( log₂ 5) * 3

log₂ x =3*log₂ 5

log₂ x =log₂ 5³

x=5³

x=125

b)

5^(log₂₅ 2)

x=5^(log₂₅ 2)

log₂₅ x=log₂₅  5^(log₂₅ 2)

log₂₅ x=(log₂₅ 2) *log₂₅  5

log₂₅ x=(log₂₅ 2) * (log  5 /log 25)

log₂₅ x=(log₂₅ 2) * (log  5 /log 5²)

log₂₅ x=(log₂₅ 2) * (log  5 /2*log 5)

log₂₅ x=(log₂₅ 2) * (1/2)

log₂₅ x=(1/2) * (log₂₅ 2)

log₂₅ x= (log₂₅ 2^(1/2))  

log₂₅ x= (log₂₅ √2 )  

x=√2