Rekenen met log₁₀ (reeks 1)

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Bereken

1. \(\log \frac{1}{10^{5}}\)
2. \(\log 1000000\)
3. \(\log \sqrt[5]{ \left(\frac{1}{10}\right)^{9} }\)
4. \(\log \sqrt[7]{ 10^{6} }\)
5. \(\log 10\)
6. \(\log 1000000000\)
7. \(\log \left(\frac{1}{10}\right)^{3}\)
8. \(\log \frac{1}{10^{2}}\)
9. \(\log \frac{1}{10^{3}}\)
10. \(\log 100\)
11. \(\log \sqrt[6]{ 10^{7} }\)
12. \(\log \sqrt{ \left(\frac{1}{10}\right)^{3} } \)

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Bereken

Verbetersleutel

1. \(\log \frac{1}{10^{5}}= \log 10^{-5}=-5\)
2. \(\log 1000000= \log 10^{6}=6\)
3. \(\log \sqrt[5]{ \left(\frac{1}{10}\right)^{9} }=\log 10^{\frac{-9}{5}}=\frac{-9}{5}\)
4. \(\log \sqrt[7]{ 10^{6} }=\log 10^{\frac{6}{7}}=\frac{6}{7}\)
5. \(\log 10= \log 10^{1}=1\)
6. \(\log 1000000000= \log 10^{9}=9\)
7. \(\log \left(\frac{1}{10}\right)^{3}=\log 10^{\frac{-3}{1}}=\frac{-3}{1}\)
8. \(\log \frac{1}{10^{2}}= \log 10^{-2}=-2\)
9. \(\log \frac{1}{10^{3}}= \log 10^{-3}=-3\)
10. \(\log 100= \log 10^{2}=2\)
11. \(\log \sqrt[6]{ 10^{7} }=\log 10^{\frac{7}{6}}=\frac{7}{6}\)
12. \(\log \sqrt{ \left(\frac{1}{10}\right)^{3} } =\log 10^{\frac{-3}{2}}=\frac{-3}{2}\)