Question

Achar o valor da expressão: (Função Logarítmica)
$M=log_\frac{1}{3} (3\sqrt{3})-log_{2}\frac{1}{4}-log_{5}5$

Answer 1

Explicação passo-a-passo:

Temos que:

• $\sf log_{\frac{1}{3}}~3\sqrt{3}=log_{3^{-1}}~\sqrt{27}$

$\sf log_{\frac{1}{3}}~3\sqrt{3}=log_{3^{-1}}~\sqrt{3^3}$

$\sf log_{\frac{1}{3}}~3\sqrt{3}=log_{3^{-1}}~3^{\frac{3}{2}}$

$\sf log_{\frac{1}{3}}~3\sqrt{3}=\dfrac{\frac{3}{2}}{-1}\cdot log_{3}~3$

$\sf log_{\frac{1}{3}}~3\sqrt{3}=\dfrac{-3}{2}\cdot1$

$\sf log_{\frac{1}{3}}~3\sqrt{3}=\dfrac{-3}{2}$

• $\sf log_{2}~\dfrac{1}{4}=log_{2}~2^{-2}$

$\sf log_{2}~\dfrac{1}{4}=(-2)\cdot log_{2}~2$

$\sf log_{2}~\dfrac{1}{4}=(-2)\cdot1$

$\sf log_{2}~\dfrac{1}{4}=-2$

• $\sf log_{5}~5=1$

Logo:

$\sf M=log_{\frac{1}{3}}~3\sqrt{3}-log_{2}~\dfrac{1}{4}-log_{5}~5$

$\sf M=\dfrac{-3}{2}-(-2)-1$

$\sf M=\dfrac{-3}{2}+2-1$

$\sf M=\dfrac{-3}{2}+1$

$\sf M=\dfrac{-3+2}{2}$

$\sf \red{M=\dfrac{-1}{2}}$

Answer 2

Resposta:

$\text{\sf Leia abaixo}$

Explicação passo-a-passo:

$\sf M = log_{\frac{1}{3}}\:3\sqrt{3} - log_2\:\dfrac{1}{4} - log_5\:5$

$\sf M = log_{\frac{1}{3}}\:3.3^{\frac{1}{2}} - log_2\:2^{-2} - log_5\:5$

$\sf M = log_{\frac{1}{3}}\:3^{\frac{3}{2}} - log_2\:2^{-2} - log_5\:5$

$\sf M = -\dfrac{3}{2} - (-2) - 1$

$\sf M = -\dfrac{3}{2} + 2 - 1$

$\boxed{\boxed{\sf M = -\dfrac{1}{2}}}$