Rekenen met log₁₀ (reeks 2)

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Bepaal x

1. \(\log x = -1\)
2. \(\log x = -5\)
3. \(\log x = \frac{-5}{6}\)
4. \(\log x = \frac{10}{9}\)
5. \(\log x = \frac{11}{10}\)
6. \(\log x = -3\)
7. \(\log x = \frac{-2}{5}\)
8. \(\log x = \frac{-11}{8}\)
9. \(\log x = 6\)
10. \(\log x = \frac{2}{3}\)
11. \(\log x = 2\)
12. \(\log x = \frac{1}{4}\)

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Bepaal x

Verbetersleutel

1. \(\log x = -1\\ \Leftrightarrow x = 10^{-1} \\ \Leftrightarrow x =0{,}1\)
2. \(\log x = -5\\ \Leftrightarrow x = \log 10^{-5} \\ \Leftrightarrow x = \frac{1}{10^{5}}\)
3. \(\log x = \frac{-5}{6}\\ \Leftrightarrow x =\log 10^{\frac{-5}{6}}\\ \Leftrightarrow x =\sqrt[6]{ \frac{1}{10^{5}} }\)
4. \(\log x = \frac{10}{9}\\ \Leftrightarrow x =\log 10^{\frac{10}{9}}\\ \Leftrightarrow x =\sqrt[9]{ 10^{10} }\)
5. \(\log x = \frac{11}{10}\\ \Leftrightarrow x =\log 10^{\frac{11}{10}}\\ \Leftrightarrow x =\sqrt[10]{ 10^{11} }\)
6. \(\log x = -3\\ \Leftrightarrow x = 10^{-3} \\ \Leftrightarrow x =0{,}001\)
7. \(\log x = \frac{-2}{5}\\ \Leftrightarrow x =\log 10^{\frac{-2}{5}}\\ \Leftrightarrow x =\sqrt[5]{ \frac{1}{10^{2}} }\)
8. \(\log x = \frac{-11}{8}\\ \Leftrightarrow x =\log 10^{\frac{-11}{8}}\\ \Leftrightarrow x =\sqrt[8]{ \frac{1}{10^{11}} }\)
9. \(\log x = 6\\ \Leftrightarrow x = 10^{6} \\ \Leftrightarrow x =1000000\)
10. \(\log x = \frac{2}{3}\\ \Leftrightarrow x =\log 10^{\frac{2}{3}}\\ \Leftrightarrow x =\sqrt[3]{ 10^{2} }\)
11. \(\log x = 2\\ \Leftrightarrow x = 10^{2} \\ \Leftrightarrow x =100\)
12. \(\log x = \frac{1}{4}\\ \Leftrightarrow x =\log 10^{\frac{1}{4}}\\ \Leftrightarrow x =\sqrt[4]{ 10 }\)