Rekenen met log₁₀ (reeks 1)

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Bereken

1. \(\log \sqrt[6]{ 10 }\)
2. \(\log 1000\)
3. \(\log 100000\)
4. \(\log \sqrt[11]{ \frac{1}{10^{8}} }\)
5. \(\log \sqrt[12]{ \frac{1}{10^{5}} }\)
6. \(\log 10000000\)
7. \(\log \frac{1}{10^{2}}\)
8. \(\log \frac{1}{10^{4}}\)
9. \(\log 100000000\)
10. \(\log \sqrt[4]{ \left(\frac{1}{10}\right) }\)
11. \(\log \sqrt[9]{ 10^{8} }\)
12. \(\log \sqrt[4]{ 10^{11} }\)

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Bereken

Verbetersleutel

1. \(\log \sqrt[6]{ 10 }=\log 10^{\frac{1}{6}}=\frac{1}{6}\)
2. \(\log 1000= \log 10^{3}=3\)
3. \(\log 100000= \log 10^{5}=5\)
4. \(\log \sqrt[11]{ \frac{1}{10^{8}} }=\log 10^{\frac{-8}{11}}=\frac{-8}{11}\)
5. \(\log \sqrt[12]{ \frac{1}{10^{5}} }=\log 10^{\frac{-5}{12}}=\frac{-5}{12}\)
6. \(\log 10000000= \log 10^{7}=7\)
7. \(\log \frac{1}{10^{2}}= \log 10^{-2}=-2\)
8. \(\log \frac{1}{10^{4}}= \log 10^{-4}=-4\)
9. \(\log 100000000= \log 10^{8}=8\)
10. \(\log \sqrt[4]{ \left(\frac{1}{10}\right) }=\log 10^{\frac{-1}{4}}=\frac{-1}{4}\)
11. \(\log \sqrt[9]{ 10^{8} }=\log 10^{\frac{8}{9}}=\frac{8}{9}\)
12. \(\log \sqrt[4]{ 10^{11} }=\log 10^{\frac{11}{4}}=\frac{11}{4}\)