Rekenen met log₁₀ (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\log 1000= \log 10^{3}=3\)
2. \(\log \frac{1}{10^{5}}= \log 10^{-5}=-5\)
3. \(\log \frac{1}{10^{6}}= \log 10^{-6}=-6\)
4. \(\log \sqrt{ \frac{1}{10^{1}} } =\log 10^{\frac{-1}{2}}=\frac{-1}{2}\)
5. \(\log 1= \log 10^{0}=0\)
6. \(\log \frac{1}{10^{3}}= \log 10^{-3}=-3\)
7. \(\log \sqrt[4]{ \frac{1}{10^{1}} }=\log 10^{\frac{-1}{4}}=\frac{-1}{4}\)
8. \(\log \frac{1}{10^{2}}= \log 10^{-2}=-2\)
9. \(\log \sqrt[7]{ 10^{8} }=\log 10^{\frac{8}{7}}=\frac{8}{7}\)
10. \(\log \sqrt[7]{ \frac{1}{10^{12}} }=\log 10^{\frac{-12}{7}}=\frac{-12}{7}\)
11. \(\log \sqrt[7]{ \frac{1}{10^{4}} }=\log 10^{\frac{-4}{7}}=\frac{-4}{7}\)
12. \(\log 10^{2}=\log 10^{\frac{2}{1}}=\frac{2}{1}\)