Question

Sendo log 2 = a e log 3 = b, calcule: Log 1,2 Log 20 Log √ 6

Answer 1

Explicação passo-a-passo:

a) $\sf log~1,2=log~\dfrac{12}{10}$

$\sf log~1,2=log~12-log~10$

$\sf log~1,2=log~(2^2\cdot3)-1$

$\sf log~1,2=2\cdot log~2+log~3-1$

$\sf log~1,2=2a+b-1$

b) $\sf log~20=log~(2\cdot10)$

$\sf log~20=log~2+log~10$

$\sf log~20=a+1$

c) $\sf log~\sqrt{6}=log~(2\cdot3)^{\frac{1}{2}}$

$\sf log~\sqrt{6}=\dfrac{1}{2}\cdot(log~2+log~3)$

$\sf log~\sqrt{6}=\dfrac{a+b}{2}$