[tex]4 - \frac{1}{2} + 27 - \frac{1}{3} = 3\frac{1}{2} + 26\frac{2}{3} = 3\frac{3}{6} + 26\frac{4}{6} =29\frac{7}{6} =30\frac{1}{6} \\\\ log_3 \ 27 = log_3 \ 3^3 = 3 \cdot log_3 \ 3 = 3 \cdot 1 = 3 \\\\ log_{\frac{1}{3}} \ 27= log_{\frac{1}{3}} \ 3^3 = log_{\frac{1}{3}} \ (\frac{1}{3})^{-3} = - 3 \cdot log_{\frac{1}{3}} \ \frac{1}{3} = - 3 \cdot 1 = -3[/tex]
1. 4-1/2+27-1/3=4+27-1/2-1/3=31-3/6-2/6=31-5/6=30 1/6
2. log3 27=log3 (3³)=3log3 3=3·1=3
3. log1/3 27=log3^-1 (3³)=-1·3log3 3=-3·1=-3
