Soal Menyederhanakan dan Menghitung Hasil Operasi Logaritma

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opan
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Soal Menyederhanakan dan Menghitung Hasil Operasi Logaritma

Post by opan » Wed Jan 30, 2019 10:27 am

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}

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