Rekenen met log₁₀ (reeks 1)

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Bereken

1. \(\log \sqrt[9]{ 10^{2} }\)
2. \(\log \frac{1}{10^{8}}\)
3. \(\log \frac{1}{10^{4}}\)
4. \(\log \frac{1}{10^{2}}\)
5. \(\log \frac{1}{10^{7}}\)
6. \(\log \sqrt{ \left(\frac{1}{10}\right) } \)
7. \(\log \sqrt[3]{ 10^{5} }\)
8. \(\log 10^{2}\)
9. \(\log \left(\frac{1}{10}\right)^{2}\)
10. \(\log 1000\)
11. \(\log 10000\)
12. \(\log 10\)

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Bereken

Verbetersleutel

1. \(\log \sqrt[9]{ 10^{2} }=\log 10^{\frac{2}{9}}=\frac{2}{9}\)
2. \(\log \frac{1}{10^{8}}= \log 10^{-8}=-8\)
3. \(\log \frac{1}{10^{4}}= \log 10^{-4}=-4\)
4. \(\log \frac{1}{10^{2}}= \log 10^{-2}=-2\)
5. \(\log \frac{1}{10^{7}}= \log 10^{-7}=-7\)
6. \(\log \sqrt{ \left(\frac{1}{10}\right) } =\log 10^{\frac{-1}{2}}=\frac{-1}{2}\)
7. \(\log \sqrt[3]{ 10^{5} }=\log 10^{\frac{5}{3}}=\frac{5}{3}\)
8. \(\log 10^{2}=\log 10^{\frac{2}{1}}=\frac{2}{1}\)
9. \(\log \left(\frac{1}{10}\right)^{2}=\log 10^{\frac{-2}{1}}=\frac{-2}{1}\)
10. \(\log 1000= \log 10^{3}=3\)
11. \(\log 10000= \log 10^{4}=4\)
12. \(\log 10= \log 10^{1}=1\)