Question
Find the value of:$\frac{\log \sqrt{8}}{8}$
✓
Answer
$\frac{\log \sqrt{8}}{8}$
$=\frac{\log 2 \sqrt{2}}{8}$
$=\frac{1}{8}(\log 2+\log \sqrt{2})$
$=\frac{1}{8}\left(\log 2+\log 2^{\frac{1}{2}}\right)$
$=\frac{1}{8} \log 2+\frac{1}{8} \log 2^{\frac{1}{2}}$
$=\frac{1}{8} \log 2+\frac{1}{2} \frac{1}{8} \log 2$
$=\frac{1}{8} \log 2+\frac{1}{16} \log 2$
$=\frac{2}{16} \log 2+\frac{1}{16} \log 2$
$=\frac{3}{16} \log 2 .$
$=\frac{\log 2 \sqrt{2}}{8}$
$=\frac{1}{8}(\log 2+\log \sqrt{2})$
$=\frac{1}{8}\left(\log 2+\log 2^{\frac{1}{2}}\right)$
$=\frac{1}{8} \log 2+\frac{1}{8} \log 2^{\frac{1}{2}}$
$=\frac{1}{8} \log 2+\frac{1}{2} \frac{1}{8} \log 2$
$=\frac{1}{8} \log 2+\frac{1}{16} \log 2$
$=\frac{2}{16} \log 2+\frac{1}{16} \log 2$
$=\frac{3}{16} \log 2 .$
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