Odpowiedź:
[tex] log_{3}(36) - 2 log_{3}( \sqrt{12} ) + log_{ \sqrt{3} }( \frac{1}{3} ) \\ [/tex]
[tex]log_{3}(36) = log_{3}( {6}^{2} ) = 2 log_{3}(6) = 2 log_{3}(2 \times 3) = 2 ( log_{3}(3) + log_{3}(2) ) = 2(1 + log_{3}(2) ) = 2 + 2 log_{3}(2) [/tex]
[tex]2 log_{3}( \sqrt{12} ) = 2 log_{3}(2 \sqrt{3} ) = 2( log_{3}(2) + log_{3}( \sqrt{3} ) ) = 2( log_{3}(2) + log_{3}( {3}^{ \frac{1}{2} } ) ) = 2( log_{3}(2) + \frac{1}{2} ) = 2 log_{3}(2) + 1[/tex]
[tex] log_{ \sqrt{3} }( \frac{1}{3} ) = log_{ {3}^{ \frac{1}{2} } }( {3}^{ - 1} ) = - 2 [/tex]
[tex]2 + 2 log_{3}(2) - 2 log_{3}(2) - 1 - 2 = 1 - 2 = - 1[/tex]
