Rekenen met log₁₀ (reeks 2)

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Bepaal x

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

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Bepaal x

Verbetersleutel

1. \(\log x = \frac{4}{9}\\ \Leftrightarrow x =\log 10^{\frac{4}{9}}\\ \Leftrightarrow x =\sqrt[9]{ 10^{4} }\)
2. \(\log x = -4\\ \Leftrightarrow x = \log 10^{-4} \\ \Leftrightarrow x = \frac{1}{10^{4}}\)
3. \(\log x = 4\\ \Leftrightarrow x = 10^{4} \\ \Leftrightarrow x =10000\)
4. \(\log x = 3\\ \Leftrightarrow x = 10^{3} \\ \Leftrightarrow x =1000\)
5. \(\log x = \frac{11}{3}\\ \Leftrightarrow x =\log 10^{\frac{11}{3}}\\ \Leftrightarrow x =\sqrt[3]{ 10^{11} }\)
6. \(\log x = \frac{11}{2}\\ \Leftrightarrow x =\log 10^{\frac{11}{2}}\\ \Leftrightarrow x = \sqrt{ 10^{11} } \)
7. \(\log x = \frac{-3}{5}\\ \Leftrightarrow x =\log 10^{\frac{-3}{5}}\\ \Leftrightarrow x =\sqrt[5]{ \frac{1}{10^{3}} }\)
8. \(\log x = -2\\ \Leftrightarrow x = 10^{-2} \\ \Leftrightarrow x =0,01\)
9. \(\log x = \frac{1}{4}\\ \Leftrightarrow x =\log 10^{\frac{1}{4}}\\ \Leftrightarrow x =\sqrt[4]{ 10 }\)
10. \(\log x = 1\\ \Leftrightarrow x = 10^{1} \\ \Leftrightarrow x =10\)
11. \(\log x = -5\\ \Leftrightarrow x = \log 10^{-5} \\ \Leftrightarrow x = \frac{1}{10^{5}}\)
12. \(\log x = -3\\ \Leftrightarrow x = \log 10^{-3} \\ \Leftrightarrow x = \frac{1}{10^{3}}\)