Rekenen met log₁₀ (reeks 1)

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Bereken

1. \(\log \sqrt[11]{ 10^{3} }\)
2. \(\log 0{,}1\)
3. \(\log \sqrt[9]{ \left(\frac{1}{10}\right)^{11} }\)
4. \(\log 10000000\)
5. \(\log \sqrt[9]{ 10^{7} }\)
6. \(\log 0{,}001\)
7. \(\log \frac{1}{10^{7}}\)
8. \(\log 10000\)
9. \(\log \frac{1}{10^{8}}\)
10. \(\log \sqrt{ \frac{1}{10^{5}} } \)
11. \(\log \sqrt[4]{ \left(\frac{1}{10}\right)^{3} }\)
12. \(\log 1\)

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Bereken

Verbetersleutel

1. \(\log \sqrt[11]{ 10^{3} }=\log 10^{\frac{3}{11}}=\frac{3}{11}\)
2. \(\log 0{,}1= \log 10^{-1}=-1\)
3. \(\log \sqrt[9]{ \left(\frac{1}{10}\right)^{11} }=\log 10^{\frac{-11}{9}}=\frac{-11}{9}\)
4. \(\log 10000000= \log 10^{7}=7\)
5. \(\log \sqrt[9]{ 10^{7} }=\log 10^{\frac{7}{9}}=\frac{7}{9}\)
6. \(\log 0{,}001= \log 10^{-3}=-3\)
7. \(\log \frac{1}{10^{7}}= \log 10^{-7}=-7\)
8. \(\log 10000= \log 10^{4}=4\)
9. \(\log \frac{1}{10^{8}}= \log 10^{-8}=-8\)
10. \(\log \sqrt{ \frac{1}{10^{5}} } =\log 10^{\frac{-5}{2}}=\frac{-5}{2}\)
11. \(\log \sqrt[4]{ \left(\frac{1}{10}\right)^{3} }=\log 10^{\frac{-3}{4}}=\frac{-3}{4}\)
12. \(\log 1= \log 10^{0}=0\)