Rekenen met log₁₀ (reeks 1)

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Bereken

1. \(\log 1000000000\)
2. \(\log \sqrt[4]{ 10^{11} }\)
3. \(\log \sqrt[11]{ \frac{1}{10^{1}} }\)
4. \(\log \frac{1}{10^{6}}\)
5. \(\log \sqrt[11]{ \frac{1}{10^{6}} }\)
6. \(\log \sqrt[7]{ \left(\frac{1}{10}\right)^{3} }\)
7. \(\log 100000\)
8. \(\log \sqrt[5]{ \left(\frac{1}{10}\right)^{8} }\)
9. \(\log 10^{3}\)
10. \(\log \sqrt[9]{ \left(\frac{1}{10}\right)^{7} }\)
11. \(\log \sqrt[7]{ 10^{4} }\)
12. \(\log \sqrt{ \left(\frac{1}{10}\right)^{3} } \)

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Bereken

Verbetersleutel

1. \(\log 1000000000= \log 10^{9}=9\)
2. \(\log \sqrt[4]{ 10^{11} }=\log 10^{\frac{11}{4}}=\frac{11}{4}\)
3. \(\log \sqrt[11]{ \frac{1}{10^{1}} }=\log 10^{\frac{-1}{11}}=\frac{-1}{11}\)
4. \(\log \frac{1}{10^{6}}= \log 10^{-6}=-6\)
5. \(\log \sqrt[11]{ \frac{1}{10^{6}} }=\log 10^{\frac{-6}{11}}=\frac{-6}{11}\)
6. \(\log \sqrt[7]{ \left(\frac{1}{10}\right)^{3} }=\log 10^{\frac{-3}{7}}=\frac{-3}{7}\)
7. \(\log 100000= \log 10^{5}=5\)
8. \(\log \sqrt[5]{ \left(\frac{1}{10}\right)^{8} }=\log 10^{\frac{-8}{5}}=\frac{-8}{5}\)
9. \(\log 10^{3}=\log 10^{\frac{3}{1}}=\frac{3}{1}\)
10. \(\log \sqrt[9]{ \left(\frac{1}{10}\right)^{7} }=\log 10^{\frac{-7}{9}}=\frac{-7}{9}\)
11. \(\log \sqrt[7]{ 10^{4} }=\log 10^{\frac{4}{7}}=\frac{4}{7}\)
12. \(\log \sqrt{ \left(\frac{1}{10}\right)^{3} } =\log 10^{\frac{-3}{2}}=\frac{-3}{2}\)