Question

como resolver LOG da raiz de 3 na base 1/9?

Answer 1

Boa noite!
Solução!

$log_{ \dfrac{1}{9} } \sqrt{3}$

$log_{ \dfrac{1}{9} } \sqrt{3}=x$

$\sqrt{3}= \left ( \frac{1}{9} \right )^{x}$

$(3)^{ \dfrac{1}{2} } = \left ( \dfrac{1}{3^{2} } \right )^{x}$

$(3)^{ \dfrac{1}{2} }=(3^{-2} ) ^{x}$

$(3)^{ \dfrac{1}{2} }=(3 ) ^{-2x}$

$\dfrac{1}{2} =-2x$

$x= -\dfrac{1}{4}$

Boa noite!
Bons estudos!

Answer 2

Outra...

$\log_{\frac{1}{9}} \sqrt{3} = \\\\ \log_{\frac{1}{3^2}} 3^{\frac{1}{2}} = \\\\ \log_{3^{-2}} 3^{\frac{1}{2}} = \\\\\frac{1}{-2}\cdot\frac{1}{2}\cdot\log_33=\\\\\boxed{-\frac{1}{4}}$