Rekenen met log₁₀ (reeks 1)

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Bereken

1. \(\log \frac{1}{10^{5}}\)
2. \(\log \frac{1}{10^{1}}\)
3. \(\log \frac{1}{10^{7}}\)
4. \(\log \frac{1}{10^{9}}\)
5. \(\log \sqrt[4]{ \frac{1}{10^{3}} }\)
6. \(\log \frac{1}{10^{4}}\)
7. \(\log 0{,}001\)
8. \(\log 1000000\)
9. \(\log \sqrt[10]{ 10^{11} }\)
10. \(\log \sqrt[4]{ 10^{5} }\)
11. \(\log \sqrt[7]{ \left(\frac{1}{10}\right)^{4} }\)
12. \(\log \sqrt[4]{ 10^{3} }\)

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Bereken

Verbetersleutel

1. \(\log \frac{1}{10^{5}}= \log 10^{-5}=-5\)
2. \(\log \frac{1}{10^{1}}= \log 10^{-1}=-1\)
3. \(\log \frac{1}{10^{7}}= \log 10^{-7}=-7\)
4. \(\log \frac{1}{10^{9}}= \log 10^{-9}=-9\)
5. \(\log \sqrt[4]{ \frac{1}{10^{3}} }=\log 10^{\frac{-3}{4}}=\frac{-3}{4}\)
6. \(\log \frac{1}{10^{4}}= \log 10^{-4}=-4\)
7. \(\log 0{,}001= \log 10^{-3}=-3\)
8. \(\log 1000000= \log 10^{6}=6\)
9. \(\log \sqrt[10]{ 10^{11} }=\log 10^{\frac{11}{10}}=\frac{11}{10}\)
10. \(\log \sqrt[4]{ 10^{5} }=\log 10^{\frac{5}{4}}=\frac{5}{4}\)
11. \(\log \sqrt[7]{ \left(\frac{1}{10}\right)^{4} }=\log 10^{\frac{-4}{7}}=\frac{-4}{7}\)
12. \(\log \sqrt[4]{ 10^{3} }=\log 10^{\frac{3}{4}}=\frac{3}{4}\)