Rekenen met log₁₀ (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\log \sqrt{ 10^{5} } =\log 10^{\frac{5}{2}}=\frac{5}{2}\)
2. \(\log \sqrt[3]{ 10^{7} }=\log 10^{\frac{7}{3}}=\frac{7}{3}\)
3. \(\log \sqrt[3]{ \left(\frac{1}{10}\right)^{4} }=\log 10^{\frac{-4}{3}}=\frac{-4}{3}\)
4. \(\log 10000000= \log 10^{7}=7\)
5. \(\log \sqrt{ \left(\frac{1}{10}\right) } =\log 10^{\frac{-1}{2}}=\frac{-1}{2}\)
6. \(\log \sqrt{ \frac{1}{10^{11}} } =\log 10^{\frac{-11}{2}}=\frac{-11}{2}\)
7. \(\log \sqrt[7]{ 10^{5} }=\log 10^{\frac{5}{7}}=\frac{5}{7}\)
8. \(\log \frac{1}{10^{5}}= \log 10^{-5}=-5\)
9. \(\log \frac{1}{10^{4}}= \log 10^{-4}=-4\)
10. \(\log 1000000000= \log 10^{9}=9\)
11. \(\log \sqrt[12]{ \frac{1}{10^{1}} }=\log 10^{\frac{-1}{12}}=\frac{-1}{12}\)
12. \(\log 1= \log 10^{0}=0\)