Rekenen met log₁₀ (reeks 1)

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Bereken

1. \(\log \sqrt[5]{ \frac{1}{10^{1}} }\)
2. \(\log 100000\)
3. \(\log 10^{3}\)
4. \(\log \sqrt[8]{ \frac{1}{10^{9}} }\)
5. \(\log \sqrt{ \left(\frac{1}{10}\right)^{5} } \)
6. \(\log 1000000\)
7. \(\log \frac{1}{10^{8}}\)
8. \(\log 100000000\)
9. \(\log \frac{1}{10^{2}}\)
10. \(\log \frac{1}{10^{7}}\)
11. \(\log \sqrt[5]{ \frac{1}{10^{6}} }\)
12. \(\log 1\)

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Bereken

Verbetersleutel

1. \(\log \sqrt[5]{ \frac{1}{10^{1}} }=\log 10^{\frac{-1}{5}}=\frac{-1}{5}\)
2. \(\log 100000= \log 10^{5}=5\)
3. \(\log 10^{3}=\log 10^{\frac{3}{1}}=\frac{3}{1}\)
4. \(\log \sqrt[8]{ \frac{1}{10^{9}} }=\log 10^{\frac{-9}{8}}=\frac{-9}{8}\)
5. \(\log \sqrt{ \left(\frac{1}{10}\right)^{5} } =\log 10^{\frac{-5}{2}}=\frac{-5}{2}\)
6. \(\log 1000000= \log 10^{6}=6\)
7. \(\log \frac{1}{10^{8}}= \log 10^{-8}=-8\)
8. \(\log 100000000= \log 10^{8}=8\)
9. \(\log \frac{1}{10^{2}}= \log 10^{-2}=-2\)
10. \(\log \frac{1}{10^{7}}= \log 10^{-7}=-7\)
11. \(\log \sqrt[5]{ \frac{1}{10^{6}} }=\log 10^{\frac{-6}{5}}=\frac{-6}{5}\)
12. \(\log 1= \log 10^{0}=0\)