Rekenen met log₁₀ (reeks 2)

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Bepaal x

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

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Bepaal x

Verbetersleutel

1. \(\log x = -1\\ \Leftrightarrow x = 10^{-1} \\ \Leftrightarrow x =0,1\)
2. \(\log x = 6\\ \Leftrightarrow x = 10^{6} \\ \Leftrightarrow x =1000000\)
3. \(\log x = 5\\ \Leftrightarrow x = 10^{5} \\ \Leftrightarrow x =100000\)
4. \(\log x = \frac{-5}{9}\\ \Leftrightarrow x =\log 10^{\frac{-5}{9}}\\ \Leftrightarrow x =\sqrt[9]{ \frac{1}{10^{5}} }\)
5. \(\log x = \frac{-3}{1}\\ \Leftrightarrow x =\log 10^{\frac{-3}{1}}\\ \Leftrightarrow x =\frac{1}{10^{3}}\)
6. \(\log x = \frac{-8}{3}\\ \Leftrightarrow x =\log 10^{\frac{-8}{3}}\\ \Leftrightarrow x =\sqrt[3]{ \frac{1}{10^{8}} }\)
7. \(\log x = \frac{-2}{1}\\ \Leftrightarrow x =\log 10^{\frac{-2}{1}}\\ \Leftrightarrow x =\frac{1}{10^{2}}\)
8. \(\log x = \frac{5}{2}\\ \Leftrightarrow x =\log 10^{\frac{5}{2}}\\ \Leftrightarrow x = \sqrt{ 10^{5} } \)
9. \(\log x = \frac{1}{4}\\ \Leftrightarrow x =\log 10^{\frac{1}{4}}\\ \Leftrightarrow x =\sqrt[4]{ 10 }\)
10. \(\log x = 4\\ \Leftrightarrow x = 10^{4} \\ \Leftrightarrow x =10000\)
11. \(\log x = 7\\ \Leftrightarrow x = 10^{7} \\ \Leftrightarrow x =10000000\)
12. \(\log x = \frac{4}{3}\\ \Leftrightarrow x =\log 10^{\frac{4}{3}}\\ \Leftrightarrow x =\sqrt[3]{ 10^{4} }\)