Rekenen met log₁₀ (reeks 2)

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Bepaal x

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

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Bepaal x

Verbetersleutel

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