Rekenen met log₁₀ (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

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