Rekenen met log₁₀ (reeks 2)

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Bepaal x

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

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Bepaal x

Verbetersleutel

1. \(\log x = -8\\ \Leftrightarrow x = \log 10^{-8} \\ \Leftrightarrow x = \frac{1}{10^{8}}\)
2. \(\log x = 5\\ \Leftrightarrow x = 10^{5} \\ \Leftrightarrow x =100000\)
3. \(\log x = \frac{2}{9}\\ \Leftrightarrow x =\log 10^{\frac{2}{9}}\\ \Leftrightarrow x =\sqrt[9]{ 10^{2} }\)
4. \(\log x = \frac{1}{3}\\ \Leftrightarrow x =\log 10^{\frac{1}{3}}\\ \Leftrightarrow x =\sqrt[3]{ 10 }\)
5. \(\log x = \frac{-1}{7}\\ \Leftrightarrow x =\log 10^{\frac{-1}{7}}\\ \Leftrightarrow x =\sqrt[7]{ \frac{1}{10^{1}} }\)
6. \(\log x = 2\\ \Leftrightarrow x = 10^{2} \\ \Leftrightarrow x =100\)
7. \(\log x = \frac{11}{5}\\ \Leftrightarrow x =\log 10^{\frac{11}{5}}\\ \Leftrightarrow x =\sqrt[5]{ 10^{11} }\)
8. \(\log x = -9\\ \Leftrightarrow x = \log 10^{-9} \\ \Leftrightarrow x = \frac{1}{10^{9}}\)
9. \(\log x = \frac{-7}{9}\\ \Leftrightarrow x =\log 10^{\frac{-7}{9}}\\ \Leftrightarrow x =\sqrt[9]{ \frac{1}{10^{7}} }\)
10. \(\log x = \frac{3}{4}\\ \Leftrightarrow x =\log 10^{\frac{3}{4}}\\ \Leftrightarrow x =\sqrt[4]{ 10^{3} }\)
11. \(\log x = \frac{2}{1}\\ \Leftrightarrow x =\log 10^{\frac{2}{1}}\\ \Leftrightarrow x =10^{2}\)
12. \(\log x = -1\\ \Leftrightarrow x = \log 10^{-1} \\ \Leftrightarrow x = \frac{1}{10^{1}}\)