Rekenen met log₁₀ (reeks 2)

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Bepaal x

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

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Bepaal x

Verbetersleutel

1. \(\log x = \frac{7}{5}\\ \Leftrightarrow x =\log 10^{\frac{7}{5}}\\ \Leftrightarrow x =\sqrt[5]{ 10^{7} }\)
2. \(\log x = \frac{7}{3}\\ \Leftrightarrow x =\log 10^{\frac{7}{3}}\\ \Leftrightarrow x =\sqrt[3]{ 10^{7} }\)
3. \(\log x = \frac{-2}{9}\\ \Leftrightarrow x =\log 10^{\frac{-2}{9}}\\ \Leftrightarrow x =\sqrt[9]{ \frac{1}{10^{2}} }\)
4. \(\log x = 6\\ \Leftrightarrow x = 10^{6} \\ \Leftrightarrow x =1000000\)
5. \(\log x = -9\\ \Leftrightarrow x = \log 10^{-9} \\ \Leftrightarrow x = \frac{1}{10^{9}}\)
6. \(\log x = 3\\ \Leftrightarrow x = 10^{3} \\ \Leftrightarrow x =1000\)
7. \(\log x = 2\\ \Leftrightarrow x = 10^{2} \\ \Leftrightarrow x =100\)
8. \(\log x = -2\\ \Leftrightarrow x = 10^{-2} \\ \Leftrightarrow x =0,01\)
9. \(\log x = -7\\ \Leftrightarrow x = \log 10^{-7} \\ \Leftrightarrow x = \frac{1}{10^{7}}\)
10. \(\log x = \frac{3}{2}\\ \Leftrightarrow x =\log 10^{\frac{3}{2}}\\ \Leftrightarrow x = \sqrt{ 10^{3} } \)
11. \(\log x = \frac{-2}{3}\\ \Leftrightarrow x =\log 10^{\frac{-2}{3}}\\ \Leftrightarrow x =\sqrt[3]{ \frac{1}{10^{2}} }\)
12. \(\log x = \frac{-11}{2}\\ \Leftrightarrow x =\log 10^{\frac{-11}{2}}\\ \Leftrightarrow x = \sqrt{ \frac{1}{10^{11}} } \)