Rekenen met log₁₀ (reeks 2)

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Bepaal x

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

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Bepaal x

Verbetersleutel

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