Rekenen met log₁₀ (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

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