Rekenen met log₁₀ (reeks 2)

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Bepaal x

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

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Bepaal x

Verbetersleutel

1. \(\log x = -3\\ \Leftrightarrow x = \log 10^{-3} \\ \Leftrightarrow x = \frac{1}{10^{3}}\)
2. \(\log x = \frac{11}{12}\\ \Leftrightarrow x =\log 10^{\frac{11}{12}}\\ \Leftrightarrow x =\sqrt[12]{ 10^{11} }\)
3. \(\log x = 6\\ \Leftrightarrow x = 10^{6} \\ \Leftrightarrow x =1000000\)
4. \(\log x = 3\\ \Leftrightarrow x = 10^{3} \\ \Leftrightarrow x =1000\)
5. \(\log x = 2\\ \Leftrightarrow x = 10^{2} \\ \Leftrightarrow x =100\)
6. \(\log x = -1\\ \Leftrightarrow x = \log 10^{-1} \\ \Leftrightarrow x = \frac{1}{10^{1}}\)
7. \(\log x = \frac{8}{3}\\ \Leftrightarrow x =\log 10^{\frac{8}{3}}\\ \Leftrightarrow x =\sqrt[3]{ 10^{8} }\)
8. \(\log x = \frac{-3}{7}\\ \Leftrightarrow x =\log 10^{\frac{-3}{7}}\\ \Leftrightarrow x =\sqrt[7]{ \frac{1}{10^{3}} }\)
9. \(\log x = -7\\ \Leftrightarrow x = \log 10^{-7} \\ \Leftrightarrow x = \frac{1}{10^{7}}\)
10. \(\log x = \frac{12}{5}\\ \Leftrightarrow x =\log 10^{\frac{12}{5}}\\ \Leftrightarrow x =\sqrt[5]{ 10^{12} }\)
11. \(\log x = \frac{-1}{2}\\ \Leftrightarrow x =\log 10^{\frac{-1}{2}}\\ \Leftrightarrow x = \sqrt{ \frac{1}{10^{1}} } \)
12. \(\log x = -9\\ \Leftrightarrow x = \log 10^{-9} \\ \Leftrightarrow x = \frac{1}{10^{9}}\)