Rekenen met log₁₀ (reeks 2)

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Bepaal x

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

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Bepaal x

Verbetersleutel

1. \(\log x = \frac{1}{3}\\ \Leftrightarrow x =\log 10^{\frac{1}{3}}\\ \Leftrightarrow x =\sqrt[3]{ 10 }\)
2. \(\log x = \frac{-4}{7}\\ \Leftrightarrow x =\log 10^{\frac{-4}{7}}\\ \Leftrightarrow x =\sqrt[7]{ \frac{1}{10^{4}} }\)
3. \(\log x = -2\\ \Leftrightarrow x = 10^{-2} \\ \Leftrightarrow x =0,01\)
4. \(\log x = \frac{1}{2}\\ \Leftrightarrow x =\log 10^{\frac{1}{2}}\\ \Leftrightarrow x = \sqrt{ 10 } \)
5. \(\log x = -3\\ \Leftrightarrow x = \log 10^{-3} \\ \Leftrightarrow x = \frac{1}{10^{3}}\)
6. \(\log x = -1\\ \Leftrightarrow x = \log 10^{-1} \\ \Leftrightarrow x = \frac{1}{10^{1}}\)
7. \(\log x = 5\\ \Leftrightarrow x = 10^{5} \\ \Leftrightarrow x =100000\)
8. \(\log x = -7\\ \Leftrightarrow x = \log 10^{-7} \\ \Leftrightarrow x = \frac{1}{10^{7}}\)
9. \(\log x = \frac{11}{5}\\ \Leftrightarrow x =\log 10^{\frac{11}{5}}\\ \Leftrightarrow x =\sqrt[5]{ 10^{11} }\)
10. \(\log x = -9\\ \Leftrightarrow x = \log 10^{-9} \\ \Leftrightarrow x = \frac{1}{10^{9}}\)
11. \(\log x = \frac{9}{8}\\ \Leftrightarrow x =\log 10^{\frac{9}{8}}\\ \Leftrightarrow x =\sqrt[8]{ 10^{9} }\)
12. \(\log x = 4\\ \Leftrightarrow x = 10^{4} \\ \Leftrightarrow x =10000\)