Rekenen met log₁₀ (reeks 1)

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Bereken

1. \(\log \frac{1}{10^{1}}\)
2. \(\log \frac{1}{10^{9}}\)
3. \(\log \frac{1}{10^{3}}\)
4. \(\log \sqrt[11]{ 10^{7} }\)
5. \(\log 100000\)
6. \(\log \frac{1}{10^{2}}\)
7. \(\log 10000000\)
8. \(\log \sqrt[8]{ \left(\frac{1}{10}\right)^{11} }\)
9. \(\log \sqrt[5]{ \left(\frac{1}{10}\right)^{4} }\)
10. \(\log \frac{1}{10^{4}}\)
11. \(\log \sqrt[3]{ 10^{5} }\)
12. \(\log \sqrt[5]{ \left(\frac{1}{10}\right)^{2} }\)

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Bereken

Verbetersleutel

1. \(\log \frac{1}{10^{1}}= \log 10^{-1}=-1\)
2. \(\log \frac{1}{10^{9}}= \log 10^{-9}=-9\)
3. \(\log \frac{1}{10^{3}}= \log 10^{-3}=-3\)
4. \(\log \sqrt[11]{ 10^{7} }=\log 10^{\frac{7}{11}}=\frac{7}{11}\)
5. \(\log 100000= \log 10^{5}=5\)
6. \(\log \frac{1}{10^{2}}= \log 10^{-2}=-2\)
7. \(\log 10000000= \log 10^{7}=7\)
8. \(\log \sqrt[8]{ \left(\frac{1}{10}\right)^{11} }=\log 10^{\frac{-11}{8}}=\frac{-11}{8}\)
9. \(\log \sqrt[5]{ \left(\frac{1}{10}\right)^{4} }=\log 10^{\frac{-4}{5}}=\frac{-4}{5}\)
10. \(\log \frac{1}{10^{4}}= \log 10^{-4}=-4\)
11. \(\log \sqrt[3]{ 10^{5} }=\log 10^{\frac{5}{3}}=\frac{5}{3}\)
12. \(\log \sqrt[5]{ \left(\frac{1}{10}\right)^{2} }=\log 10^{\frac{-2}{5}}=\frac{-2}{5}\)