Explicație pas cu pas:
1)
[tex]log_{3}(2) - log_{3}\left( \frac{2}{27}\right) = log_{3}(2) - (log_{3}(2) - log_{3}(27)) \\ = log_{3}(2) - log_{3}(2) + log_{3}( {3}^{3} ) = 3log_{3}(3) = 3[/tex]
2)
[tex]log_{7}(3) + log_{7}\left(\frac{1}{21} \right) = log_{7}\left( 3 \times \frac{1}{21}\right) \\ = log_{7}\left(\frac{1}{7} \right) = log_{7}( {7}^{ - 1} ) = - log_{7}(7) = - 1[/tex]
3)
[tex] \frac{ log_{5}(3) - log_{5}(48) }{ log_{5}(4) } = \frac{ log_{5}( \frac{3}{48} ) }{ log_{5}( {2}^{2} ) } = \frac{ log_{5}\left(\frac{1}{16} \right) }{2 log_{5}(2) } \\ = \frac{ log_{5}( {2}^{ - 4} ) }{2 log_{5}(2) } = \frac{ - 4 log_{5}(2) }{2 log_{5}(2) } = - 2 [/tex]
4)
[tex]log_{5}(75) - log_{5}(3) + log_{7}(7) = log_{5}\left(\frac{75}{3} \right) + 1 = log_{5}(25) + 1 \\ = log_{5}( {5}^{2} ) + 1 = 2 log_{5}(5) + 1 = 2 + 1 = 3[/tex]
