Rekenen met log₁₀ (reeks 2)

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Bepaal x

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

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Bepaal x

Verbetersleutel

1. \(\log x = -7\\ \Leftrightarrow x = \log 10^{-7} \\ \Leftrightarrow x = \frac{1}{10^{7}}\)
2. \(\log x = \frac{-3}{4}\\ \Leftrightarrow x =\log 10^{\frac{-3}{4}}\\ \Leftrightarrow x =\sqrt[4]{ \frac{1}{10^{3}} }\)
3. \(\log x = -1\\ \Leftrightarrow x = \log 10^{-1} \\ \Leftrightarrow x = \frac{1}{10^{1}}\)
4. \(\log x = \frac{8}{5}\\ \Leftrightarrow x =\log 10^{\frac{8}{5}}\\ \Leftrightarrow x =\sqrt[5]{ 10^{8} }\)
5. \(\log x = -5\\ \Leftrightarrow x = \log 10^{-5} \\ \Leftrightarrow x = \frac{1}{10^{5}}\)
6. \(\log x = 1\\ \Leftrightarrow x = 10^{1} \\ \Leftrightarrow x =10\)
7. \(\log x = -8\\ \Leftrightarrow x = \log 10^{-8} \\ \Leftrightarrow x = \frac{1}{10^{8}}\)
8. \(\log x = 5\\ \Leftrightarrow x = 10^{5} \\ \Leftrightarrow x =100000\)
9. \(\log x = -2\\ \Leftrightarrow x = \log 10^{-2} \\ \Leftrightarrow x = \frac{1}{10^{2}}\)
10. \(\log x = 3\\ \Leftrightarrow x = 10^{3} \\ \Leftrightarrow x =1000\)
11. \(\log x = \frac{-1}{2}\\ \Leftrightarrow x =\log 10^{\frac{-1}{2}}\\ \Leftrightarrow x = \sqrt{ \frac{1}{10^{1}} } \)
12. \(\log x = \frac{-2}{3}\\ \Leftrightarrow x =\log 10^{\frac{-2}{3}}\\ \Leftrightarrow x =\sqrt[3]{ \frac{1}{10^{2}} }\)