Rekenen met log₁₀ (reeks 1)

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Bereken

1. \(\log \frac{1}{10^{9}}\)
2. \(\log \frac{1}{10^{6}}\)
3. \(\log \sqrt[6]{ \frac{1}{10^{11}} }\)
4. \(\log \frac{1}{10^{5}}\)
5. \(\log 1000000000\)
6. \(\log 10^{6}\)
7. \(\log \sqrt[5]{ \left(\frac{1}{10}\right)^{7} }\)
8. \(\log 0{,}1\)
9. \(\log 100\)
10. \(\log \sqrt{ 10^{3} } \)
11. \(\log 1\)
12. \(\log \sqrt[11]{ \frac{1}{10^{2}} }\)

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Bereken

Verbetersleutel

1. \(\log \frac{1}{10^{9}}= \log 10^{-9}=-9\)
2. \(\log \frac{1}{10^{6}}= \log 10^{-6}=-6\)
3. \(\log \sqrt[6]{ \frac{1}{10^{11}} }=\log 10^{\frac{-11}{6}}=\frac{-11}{6}\)
4. \(\log \frac{1}{10^{5}}= \log 10^{-5}=-5\)
5. \(\log 1000000000= \log 10^{9}=9\)
6. \(\log 10^{6}=\log 10^{\frac{6}{1}}=\frac{6}{1}\)
7. \(\log \sqrt[5]{ \left(\frac{1}{10}\right)^{7} }=\log 10^{\frac{-7}{5}}=\frac{-7}{5}\)
8. \(\log 0{,}1= \log 10^{-1}=-1\)
9. \(\log 100= \log 10^{2}=2\)
10. \(\log \sqrt{ 10^{3} } =\log 10^{\frac{3}{2}}=\frac{3}{2}\)
11. \(\log 1= \log 10^{0}=0\)
12. \(\log \sqrt[11]{ \frac{1}{10^{2}} }=\log 10^{\frac{-2}{11}}=\frac{-2}{11}\)