Rekenen met log₁₀ (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\log \sqrt[4]{ 10^{5} }=\log 10^{\frac{5}{4}}=\frac{5}{4}\)
2. \(\log 1= \log 10^{0}=0\)
3. \(\log 10000000= \log 10^{7}=7\)
4. \(\log \frac{1}{10^{9}}= \log 10^{-9}=-9\)
5. \(\log \sqrt[5]{ 10^{6} }=\log 10^{\frac{6}{5}}=\frac{6}{5}\)
6. \(\log 100= \log 10^{2}=2\)
7. \(\log \sqrt[10]{ 10^{11} }=\log 10^{\frac{11}{10}}=\frac{11}{10}\)
8. \(\log \sqrt{ 10^{3} } =\log 10^{\frac{3}{2}}=\frac{3}{2}\)
9. \(\log \sqrt[9]{ \left(\frac{1}{10}\right)^{5} }=\log 10^{\frac{-5}{9}}=\frac{-5}{9}\)
10. \(\log \frac{1}{10^{2}}= \log 10^{-2}=-2\)
11. \(\log \sqrt[4]{ 10^{3} }=\log 10^{\frac{3}{4}}=\frac{3}{4}\)
12. \(\log \frac{1}{10^{1}}= \log 10^{-1}=-1\)