Question

Se log 2 = a e log 3 = b, calcule em função de a e b os seguintes logaritmos decimais:
EXEMPLO: log 6 = log(2 ∙ 3) = log 2 + log 3 = a + b
a) log 12

b) log 2/3

c) log 1,5

d) log 144
Dica: Escreva o número 144 na forma fatorada, decompondo-o em fatores primos.

Answer 1

Explicação passo-a-passo:

a)

$\sf log~12=log~(2^2\cdot3)$

$\sf log~12=log~2^2+log~3$

$\sf log~12=2\cdot log~2+log~3$

$\boxed{\red{\sf log~12=2a+b}}$

b)

$\sf log~\Big(\dfrac{2}{3}\Big)=log~2-log~3$

$\boxed{\red{\sf log~\Big(\dfrac{2}{3}\Big)=a-b}}$

c)

$\sf log~1,5=log~\Big(\dfrac{15}{10}\Big)$

$\sf log~1,5=log~\Big(\dfrac{3}{2}\Big)$

$\sf log~1,5=log~3-log~2$

$\boxed{\red{\sf log~1,5=b-a}}$

d)

$\sf log~144=log~(2^4\cdot3^2)$

$\sf log~144=log~2^4+log~3^2$

$\sf log~144=4\cdot log~2+2\cdot log~3$

$\boxed{\red{\sf log~144=4a+2b}}$