Rekenen met log₁₀ (reeks 1)

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Bereken

1. \(\log \sqrt[10]{ \frac{1}{10^{11}} }\)
2. \(\log \frac{1}{10^{7}}\)
3. \(\log \frac{1}{10^{5}}\)
4. \(\log \frac{1}{10^{8}}\)
5. \(\log \sqrt[4]{ 10^{9} }\)
6. \(\log 0{,}001\)
7. \(\log \sqrt[3]{ 10 }\)
8. \(\log 100\)
9. \(\log 10000000\)
10. \(\log \sqrt[4]{ \left(\frac{1}{10}\right) }\)
11. \(\log \frac{1}{10^{6}}\)
12. \(\log \sqrt[11]{ 10^{2} }\)

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Bereken

Verbetersleutel

1. \(\log \sqrt[10]{ \frac{1}{10^{11}} }=\log 10^{\frac{-11}{10}}=\frac{-11}{10}\)
2. \(\log \frac{1}{10^{7}}= \log 10^{-7}=-7\)
3. \(\log \frac{1}{10^{5}}= \log 10^{-5}=-5\)
4. \(\log \frac{1}{10^{8}}= \log 10^{-8}=-8\)
5. \(\log \sqrt[4]{ 10^{9} }=\log 10^{\frac{9}{4}}=\frac{9}{4}\)
6. \(\log 0{,}001= \log 10^{-3}=-3\)
7. \(\log \sqrt[3]{ 10 }=\log 10^{\frac{1}{3}}=\frac{1}{3}\)
8. \(\log 100= \log 10^{2}=2\)
9. \(\log 10000000= \log 10^{7}=7\)
10. \(\log \sqrt[4]{ \left(\frac{1}{10}\right) }=\log 10^{\frac{-1}{4}}=\frac{-1}{4}\)
11. \(\log \frac{1}{10^{6}}= \log 10^{-6}=-6\)
12. \(\log \sqrt[11]{ 10^{2} }=\log 10^{\frac{2}{11}}=\frac{2}{11}\)