Question

Escolha uma: a. 3 b. 2 c. 5 d. 4

Answer 1

Explicação passo-a-passo:

• $\sf log_{3}~27=log_{3}~3^3$

$\sf log_{3}~27=3$

• $\sf log_{10}~0,1=log_{3}~10^{-1}$

$\sf log_{10}~0,1=-1$

• $\sf log_{2}~\sqrt{2}=log_{2}~2^{\frac{1}{2}}$

$\sf log_{2}~\sqrt{2}=\dfrac{1}{2}$

Logo:

$\sf \dfrac{log_{3}~27+log_{10}~0,1}{log_{2}~\sqrt{2}}=\dfrac{3-1}{\frac{1}{2}}$

$\sf \dfrac{log_{3}~27+log_{10}~0,1}{log_{2}~\sqrt{2}}=\dfrac{2}{\frac{1}{2}}$

$\sf \dfrac{log_{3}~27+log_{10}~0,1}{log_{2}~\sqrt{2}}=2\cdot\dfrac{2}{1}$

$\sf \dfrac{log_{3}~27+log_{10}~0,1}{log_{2}~\sqrt{2}}=4$

Letra D