Rekenen met log₁₀ (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

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