Rekenen met log₁₀ (reeks 1)

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Bereken

1. \(\log 1000000\)
2. \(\log \left(\frac{1}{10}\right)^{3}\)
3. \(\log \sqrt[9]{ \left(\frac{1}{10}\right) }\)
4. \(\log \sqrt[6]{ 10^{7} }\)
5. \(\log \sqrt[5]{ \left(\frac{1}{10}\right)^{4} }\)
6. \(\log 100000000\)
7. \(\log 1000000000\)
8. \(\log 10000\)
9. \(\log \frac{1}{10^{7}}\)
10. \(\log 10\)
11. \(\log \frac{1}{10^{5}}\)
12. \(\log \left(\frac{1}{10}\right)^{5}\)

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Bereken

Verbetersleutel

1. \(\log 1000000= \log 10^{6}=6\)
2. \(\log \left(\frac{1}{10}\right)^{3}=\log 10^{\frac{-3}{1}}=\frac{-3}{1}\)
3. \(\log \sqrt[9]{ \left(\frac{1}{10}\right) }=\log 10^{\frac{-1}{9}}=\frac{-1}{9}\)
4. \(\log \sqrt[6]{ 10^{7} }=\log 10^{\frac{7}{6}}=\frac{7}{6}\)
5. \(\log \sqrt[5]{ \left(\frac{1}{10}\right)^{4} }=\log 10^{\frac{-4}{5}}=\frac{-4}{5}\)
6. \(\log 100000000= \log 10^{8}=8\)
7. \(\log 1000000000= \log 10^{9}=9\)
8. \(\log 10000= \log 10^{4}=4\)
9. \(\log \frac{1}{10^{7}}= \log 10^{-7}=-7\)
10. \(\log 10= \log 10^{1}=1\)
11. \(\log \frac{1}{10^{5}}= \log 10^{-5}=-5\)
12. \(\log \left(\frac{1}{10}\right)^{5}=\log 10^{\frac{-5}{1}}=\frac{-5}{1}\)