Soal
Hasil $\frac{^{\sqrt{3}}\log 5\cdot ^{25}\log 3\sqrt{3}- ^4\log 16}{^3\log 54- ^3\log 2}$ adalah …
Jawaban \begin{align} \frac{^{\sqrt{3}}\log 5\cdot ^{25}\log 3\sqrt{3}- ^4\log 16}{^3\log 54- ^3\log 2} &= \frac{^{3^{\frac{1}{2}}}\log 5\cdot ^{5^2}\log 3^{\frac{3}{2}}-2}{^3\log \frac{54}{2}}\\ &= \frac{\frac{1}{\left(\frac{1}{2}\right)} ^3\log 5\cdot \frac{3}{4} ^5\log 3-2}{^3\log 27}\\ &=\frac{\left(\frac{3}{2}-2\right)}{3}\\ &=\frac{\left(-\frac{1}{2}\right)}{3}\\ &=-\frac{1}{6} \end{align}