Rekenen met log₁₀ (reeks 1)

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Bereken

1. \(\log \sqrt[10]{ 10^{11} }\)
2. \(\log \sqrt[6]{ \left(\frac{1}{10}\right)^{5} }\)
3. \(\log \sqrt[4]{ 10^{3} }\)
4. \(\log \left(\frac{1}{10}\right)^{2}\)
5. \(\log \left(\frac{1}{10}\right)^{6}\)
6. \(\log \frac{1}{10^{5}}\)
7. \(\log 100000\)
8. \(\log 1000000\)
9. \(\log 1000\)
10. \(\log \sqrt[6]{ 10^{5} }\)
11. \(\log \sqrt[10]{ \left(\frac{1}{10}\right) }\)
12. \(\log 1000000000\)

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Bereken

Verbetersleutel

1. \(\log \sqrt[10]{ 10^{11} }=\log 10^{\frac{11}{10}}=\frac{11}{10}\)
2. \(\log \sqrt[6]{ \left(\frac{1}{10}\right)^{5} }=\log 10^{\frac{-5}{6}}=\frac{-5}{6}\)
3. \(\log \sqrt[4]{ 10^{3} }=\log 10^{\frac{3}{4}}=\frac{3}{4}\)
4. \(\log \left(\frac{1}{10}\right)^{2}=\log 10^{\frac{-2}{1}}=\frac{-2}{1}\)
5. \(\log \left(\frac{1}{10}\right)^{6}=\log 10^{\frac{-6}{1}}=\frac{-6}{1}\)
6. \(\log \frac{1}{10^{5}}= \log 10^{-5}=-5\)
7. \(\log 100000= \log 10^{5}=5\)
8. \(\log 1000000= \log 10^{6}=6\)
9. \(\log 1000= \log 10^{3}=3\)
10. \(\log \sqrt[6]{ 10^{5} }=\log 10^{\frac{5}{6}}=\frac{5}{6}\)
11. \(\log \sqrt[10]{ \left(\frac{1}{10}\right) }=\log 10^{\frac{-1}{10}}=\frac{-1}{10}\)
12. \(\log 1000000000= \log 10^{9}=9\)