Question

como se resolver essa situação? 
log de  frac{1}{9} \sqrt{27} 

Answer 1

$log_{\frac{1}{9}}\sqrt{27} \\\\ \text{igualamos a uma letra qualquer} \\\\ log_{\frac{1}{9}}\sqrt{27} = x \\\\ (\frac{1}{9})^{x} = \sqrt{27} \\\\ (9)^{-x} = \sqrt{3^{3}} \\\\ (3^{2})^{-x} = \sqrt{3^{3}} \\\\ 3^{-2x} = 3^{\frac{3}{2}} \\\\ \not{3}^{-2x} = \not{3}^{\frac{3}{2}} \\\\ -2x = \frac{3}{2} \\\\ -x = \frac{\frac{3}{2}}{\frac{2}{1}} \\\\ -x = \frac{3}{4} \ \ \times -1 \\\\ \boxed{\boxed{x = -\frac{3}{4}}} \\\\\\ \therefore \boxed{log_{\frac{1}{9}}\sqrt{27} = -\frac{3}{4}}$