Rekenen met log₁₀ (reeks 2)

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Bepaal x

1. \(\log x = \frac{11}{7}\)
2. \(\log x = -5\)
3. \(\log x = -3\)
4. \(\log x = \frac{-1}{2}\)
5. \(\log x = 0\)
6. \(\log x = \frac{-5}{6}\)
7. \(\log x = -1\)
8. \(\log x = \frac{-7}{2}\)
9. \(\log x = \frac{5}{9}\)
10. \(\log x = 6\)
11. \(\log x = 5\)
12. \(\log x = \frac{5}{2}\)

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Bepaal x

Verbetersleutel

1. \(\log x = \frac{11}{7}\\ \Leftrightarrow x =\log 10^{\frac{11}{7}}\\ \Leftrightarrow x =\sqrt[7]{ 10^{11} }\)
2. \(\log x = -5\\ \Leftrightarrow x = \log 10^{-5} \\ \Leftrightarrow x = \frac{1}{10^{5}}\)
3. \(\log x = -3\\ \Leftrightarrow x = \log 10^{-3} \\ \Leftrightarrow x = \frac{1}{10^{3}}\)
4. \(\log x = \frac{-1}{2}\\ \Leftrightarrow x =\log 10^{\frac{-1}{2}}\\ \Leftrightarrow x = \sqrt{ \frac{1}{10^{1}} } \)
5. \(\log x = 0\\ \Leftrightarrow x = 10^{0} \\ \Leftrightarrow x =1\)
6. \(\log x = \frac{-5}{6}\\ \Leftrightarrow x =\log 10^{\frac{-5}{6}}\\ \Leftrightarrow x =\sqrt[6]{ \frac{1}{10^{5}} }\)
7. \(\log x = -1\\ \Leftrightarrow x = \log 10^{-1} \\ \Leftrightarrow x = \frac{1}{10^{1}}\)
8. \(\log x = \frac{-7}{2}\\ \Leftrightarrow x =\log 10^{\frac{-7}{2}}\\ \Leftrightarrow x = \sqrt{ \frac{1}{10^{7}} } \)
9. \(\log x = \frac{5}{9}\\ \Leftrightarrow x =\log 10^{\frac{5}{9}}\\ \Leftrightarrow x =\sqrt[9]{ 10^{5} }\)
10. \(\log x = 6\\ \Leftrightarrow x = 10^{6} \\ \Leftrightarrow x =1000000\)
11. \(\log x = 5\\ \Leftrightarrow x = 10^{5} \\ \Leftrightarrow x =100000\)
12. \(\log x = \frac{5}{2}\\ \Leftrightarrow x =\log 10^{\frac{5}{2}}\\ \Leftrightarrow x = \sqrt{ 10^{5} } \)