Rekenen met log₁₀ (reeks 1)

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Bereken

1. \(\log \frac{1}{10^{7}}\)
2. \(\log 0,01\)
3. \(\log 1000\)
4. \(\log \sqrt[3]{ 10 }\)
5. \(\log \sqrt[5]{ \left(\frac{1}{10}\right)^{2} }\)
6. \(\log \sqrt[3]{ \frac{1}{10^{2}} }\)
7. \(\log 0,001\)
8. \(\log 1000000000\)
9. \(\log \sqrt[3]{ 10^{8} }\)
10. \(\log \frac{1}{10^{8}}\)
11. \(\log \sqrt[6]{ 10 }\)
12. \(\log \sqrt[10]{ 10^{3} }\)

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Bereken

Verbetersleutel

1. \(\log \frac{1}{10^{7}}= \log 10^{-7}=-7\)
2. \(\log 0,01= \log 10^{-2}=-2\)
3. \(\log 1000= \log 10^{3}=3\)
4. \(\log \sqrt[3]{ 10 }=\log 10^{\frac{1}{3}}=\frac{1}{3}\)
5. \(\log \sqrt[5]{ \left(\frac{1}{10}\right)^{2} }=\log 10^{\frac{-2}{5}}=\frac{-2}{5}\)
6. \(\log \sqrt[3]{ \frac{1}{10^{2}} }=\log 10^{\frac{-2}{3}}=\frac{-2}{3}\)
7. \(\log 0,001= \log 10^{-3}=-3\)
8. \(\log 1000000000= \log 10^{9}=9\)
9. \(\log \sqrt[3]{ 10^{8} }=\log 10^{\frac{8}{3}}=\frac{8}{3}\)
10. \(\log \frac{1}{10^{8}}= \log 10^{-8}=-8\)
11. \(\log \sqrt[6]{ 10 }=\log 10^{\frac{1}{6}}=\frac{1}{6}\)
12. \(\log \sqrt[10]{ 10^{3} }=\log 10^{\frac{3}{10}}=\frac{3}{10}\)