Rekenen met log₁₀ (reeks 2)

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Bepaal x

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

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Bepaal x

Verbetersleutel

1. \(\log x = -3\\ \Leftrightarrow x = 10^{-3} \\ \Leftrightarrow x =0{,}001\)
2. \(\log x = -6\\ \Leftrightarrow x = \log 10^{-6} \\ \Leftrightarrow x = \frac{1}{10^{6}}\)
3. \(\log x = \frac{-5}{4}\\ \Leftrightarrow x =\log 10^{\frac{-5}{4}}\\ \Leftrightarrow x =\sqrt[4]{ \frac{1}{10^{5}} }\)
4. \(\log x = \frac{-4}{9}\\ \Leftrightarrow x =\log 10^{\frac{-4}{9}}\\ \Leftrightarrow x =\sqrt[9]{ \frac{1}{10^{4}} }\)
5. \(\log x = \frac{1}{3}\\ \Leftrightarrow x =\log 10^{\frac{1}{3}}\\ \Leftrightarrow x =\sqrt[3]{ 10 }\)
6. \(\log x = \frac{3}{2}\\ \Leftrightarrow x =\log 10^{\frac{3}{2}}\\ \Leftrightarrow x = \sqrt{ 10^{3} } \)
7. \(\log x = 2\\ \Leftrightarrow x = 10^{2} \\ \Leftrightarrow x =100\)
8. \(\log x = \frac{2}{1}\\ \Leftrightarrow x =\log 10^{\frac{2}{1}}\\ \Leftrightarrow x =10^{2}\)
9. \(\log x = 4\\ \Leftrightarrow x = 10^{4} \\ \Leftrightarrow x =10000\)
10. \(\log x = 3\\ \Leftrightarrow x = 10^{3} \\ \Leftrightarrow x =1000\)
11. \(\log x = \frac{7}{11}\\ \Leftrightarrow x =\log 10^{\frac{7}{11}}\\ \Leftrightarrow x =\sqrt[11]{ 10^{7} }\)
12. \(\log x = -4\\ \Leftrightarrow x = \log 10^{-4} \\ \Leftrightarrow x = \frac{1}{10^{4}}\)