Question

Aplicando as propriedades de logaritmos e sabendo que
log 2 = a e log b = 3 calcule

A) log 6 =

B) log 1,5 =

C) log 12 =

D) log 8 =

E) log 81 =

F) log 5 =

​

Answer 1

Explicação passo-a-passo:

A)

$log(6) = log(2 \times 3) = log_{}(2) + log(3) = a + b$

B)

$log(1.5) = log( \frac{3}{2} ) = log(3) - log(2) = b - a$

C)

$log(12) = log( {2}^{2} \times 3 ) = log( {2}^{2} ) + log(3) = 2 log(2) + log(3) = 2a + b$

D)

$log(8) = log( {2}^{3} ) = 3 log(2) = 3a$

E)

$log(81) = log( {3}^{4} ) = 4 log(3) = 4b$

F)

$log(5) = log( \frac{10}{2} ) = log(10) - log(2) = 1 - a$