Question

Se Ln2 = 0,6931, Ln3 = 1,0986,
pode-se afirmar corretamente que
Ln RAIZ DE 12 : / 3 O TRES TA FORA DA RAIZ
Dados: ≡ Ln de x é igual a logaritmo natural de x

Answer 1

$ln\,\left(\frac{\sqrt{12}}{3}\right)~=\\\\\\=~ln\,\left(\frac{\sqrt{2~.~2~.~3}}{3}\right)\\\\\\=~ln\,\left(\frac{\left(2~.~2~.~3\right)^{\frac{1}{2}}}{3}\right)\\\\\\Utilizando~a~propriedade~do~logaritmo~do~quociente:\\\\\\=~ln\,(2~.~2~.~3)^{\frac{1}{2}}~-~ln\,3\\\\\\Utilizando~a~propriedade~do~logaritmo~do~expoente\\\\\\=~\frac{1}{2}\,.\,ln\,(2~.~2~.~3)~-~ln\,3\\\\\\Utilizando~a~propriedade~do~logaritmo~do~produto\\\\\\=~\frac{1}{2}~.~\left(ln\,2~+~ln\,2~+~ln\,3\right)~-~ln\,3$

$=~\frac{1}{2}~.~\left(ln\,2~+~ln\,2~+~ln\,3\right)~-~ln\,3\\\\\\Substituindo~os~valores\\\\\\=~\frac{1}{2}~.~(~0,6931~+~0,6931~+~1,0986~)~-~1,0986\\\\\\=~\frac{1}{2}~.~(2,4848)~-~1,0986\\\\\\=~1,2424~-~1,0986\\\\\\=~\boxed{0,1438}$

Answer 2

Resposta:

Resposta letra C

Explicação passo-a-passo:

Tem-se que

$L_n\frac{2.3^{1/2}}{3} =L_n 2.3^{-1/2}=Ln 2 - 1/2*L_n3=$

0,6931 - ½ . 1.0986 ≈ 0,1438.