Rekenen met log₁₀ (reeks 1)

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Bereken

1. \(\log \frac{1}{10^{2}}\)
2. \(\log 1000000\)
3. \(\log \frac{1}{10^{3}}\)
4. \(\log 10\)
5. \(\log \sqrt[3]{ \frac{1}{10^{1}} }\)
6. \(\log \sqrt[6]{ \left(\frac{1}{10}\right) }\)
7. \(\log \frac{1}{10^{6}}\)
8. \(\log \frac{1}{10^{5}}\)
9. \(\log 10000000\)
10. \(\log \sqrt[7]{ 10 }\)
11. \(\log 100\)
12. \(\log 1000000000\)

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Bereken

Verbetersleutel

1. \(\log \frac{1}{10^{2}}=\log 10^{\frac{-2}{1}}=\frac{-2}{1}\)
2. \(\log 1000000= \log 10^{6}=6\)
3. \(\log \frac{1}{10^{3}}= \log 10^{-3}=-3\)
4. \(\log 10= \log 10^{1}=1\)
5. \(\log \sqrt[3]{ \frac{1}{10^{1}} }=\log 10^{\frac{-1}{3}}=\frac{-1}{3}\)
6. \(\log \sqrt[6]{ \left(\frac{1}{10}\right) }=\log 10^{\frac{-1}{6}}=\frac{-1}{6}\)
7. \(\log \frac{1}{10^{6}}= \log 10^{-6}=-6\)
8. \(\log \frac{1}{10^{5}}= \log 10^{-5}=-5\)
9. \(\log 10000000= \log 10^{7}=7\)
10. \(\log \sqrt[7]{ 10 }=\log 10^{\frac{1}{7}}=\frac{1}{7}\)
11. \(\log 100= \log 10^{2}=2\)
12. \(\log 1000000000= \log 10^{9}=9\)