Rekenen met log₁₀ (reeks 1)

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Bereken

1. \(\log \frac{1}{10^{9}}\)
2. \(\log \frac{1}{10^{1}}\)
3. \(\log \sqrt[3]{ \left(\frac{1}{10}\right)^{4} }\)
4. \(\log 0,01\)
5. \(\log \sqrt[5]{ \left(\frac{1}{10}\right)^{3} }\)
6. \(\log 1000000\)
7. \(\log \frac{1}{10^{4}}\)
8. \(\log \frac{1}{10^{6}}\)
9. \(\log 1000000000\)
10. \(\log \sqrt[5]{ 10^{8} }\)
11. \(\log \sqrt[4]{ \frac{1}{10^{3}} }\)
12. \(\log \sqrt[4]{ 10 }\)

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Bereken

Verbetersleutel

1. \(\log \frac{1}{10^{9}}= \log 10^{-9}=-9\)
2. \(\log \frac{1}{10^{1}}= \log 10^{-1}=-1\)
3. \(\log \sqrt[3]{ \left(\frac{1}{10}\right)^{4} }=\log 10^{\frac{-4}{3}}=\frac{-4}{3}\)
4. \(\log 0,01= \log 10^{-2}=-2\)
5. \(\log \sqrt[5]{ \left(\frac{1}{10}\right)^{3} }=\log 10^{\frac{-3}{5}}=\frac{-3}{5}\)
6. \(\log 1000000= \log 10^{6}=6\)
7. \(\log \frac{1}{10^{4}}= \log 10^{-4}=-4\)
8. \(\log \frac{1}{10^{6}}= \log 10^{-6}=-6\)
9. \(\log 1000000000= \log 10^{9}=9\)
10. \(\log \sqrt[5]{ 10^{8} }=\log 10^{\frac{8}{5}}=\frac{8}{5}\)
11. \(\log \sqrt[4]{ \frac{1}{10^{3}} }=\log 10^{\frac{-3}{4}}=\frac{-3}{4}\)
12. \(\log \sqrt[4]{ 10 }=\log 10^{\frac{1}{4}}=\frac{1}{4}\)