3. Vereinfache durch Zusammenfassen der Logarithmenterme. \( \begin{array}{ll}\text { a) } \log (8)+\log (5)+\log (25) & \text { d) } \log _{2}(10)+\log _{2}\left(\frac{3}{5}\right)+\log _{2}\left(\frac{1}{3}\right) \\ \text { b) } \log (150)+\log (2)-\log (3) & \text { e) } \log _{2}(7)+\log _{2}(12)-\log _{2}\left(\frac{21}{4}\right) \\ \text { c) } \log (60)-\log (2)-\log (3) & \text { f) } \log _{3}(4)+\log _{3}\left(\frac{2}{3}\right)+\log _{3}\left(\frac{1}{8}\right)\end{array} \)

a) \( \log (8) + \log (5) + \log (25) = \log (8 \cdot 5 \cdot 25) = \log (1000) \) b) \( \log (150) + \log (2) - \log (3) = \log \left( \frac{150 \cdot 2}{3} \right) = \log (100) \) c) \( \log (60) - \log (2) - \log (3) = \log \left( \frac{60}{2 \cdot 3} \right) = \log (10) \) d) \( \log_{2}(10) + \log_{2}\left(\frac{3}{5}\right) + \log_{2}\left(\frac{1}{3}\right) = \log_{2}(10) + \log_{2}\left(\frac{1}{5}\right) = \log_{2}(2) = 1 \) e) \( \log_{2}(7) + \log_{2}(12) - \log_{2}\left(\frac{21}{4}\right) = \log_{2}(7 \cdot 12) - \log_{2}(21) + \log_{2}(4) = \log_{2}(7 \cdot 12 \cdot 4 / 21) = \log_{2}(16) = 4 \) f) \( \log_{3}(4) + \log_{3}\left(\frac{2}{3}\right) + \log_{3}\left(\frac{1}{8}\right) = \log_{3}\left(4 \cdot \frac{2}{3} \cdot \frac{1}{8}\right) = \log_{3}\left(\frac{1}{3}\right) = -1 \)