Odpowiedź:
zad. 1
[tex] log_{4}(96) - log_{4}(6) = log_{4}(96 \div 6) = log_{4}(16) = log_{4}( {4}^{2} ) = 2[/tex]
D.
zad. 2
[tex]a = log_{ \frac{1}{2} }(8) = log_{ {2}^{ - 1} }( {2}^{3} ) = - 3[/tex]
[tex]b = log_{4}(8) = log_{ {2}^{2} }( {2}^{3} ) = \frac{3}{2} [/tex]
[tex]c = log_{4}( \frac{1}{2} ) = log_{ {2}^{2} }( {2}^{ - 1} ) = - \frac{1}{2} [/tex]
B, c, a
D.
zad. 3
[tex] \frac{ log_{3}(729) }{ log_{6}(36) } = \frac{ log_{3}( {3}^{6} ) }{ log_{6}( {6}^{2} ) } = \frac{6}{2} = 3[/tex]
B.
zad. 4
[tex] log_{3}( \frac{3}{2} ) + log_{3}( \frac{2}{9} ) = log_{3}( \frac{3}{2} \times \frac{2}{9} ) = log_{3}( \frac{1}{3} ) = log_{3}( {3}^{ - 1} ) = - 1[/tex]
A.
zad. 5
[tex] log_{ \sqrt{2} }(2 \sqrt{2} ) = log_{ {2}^{ \frac{1}{2} } }( {2}^{ \frac{2}{3} } ) = 3[/tex]
odp. D
zad. 6
[tex] log_{5}(0.04) - \frac{1}{2} log_{25}(5) \times log_{25}(1) = log_{5}( {5}^{ - 2} ) - \frac{1}{2} log_{ {5}^{2} }(5) \times 0 = - 2 - \frac{1}{2} \times \frac{1}{2} \times 0 = - 2 - 0 = - 2[/tex]
odp. C
zad. 7
[tex] log_{ \sqrt{2} }(2) = log_{ {2}^{ \frac{1}{2} } }(2) = 2[/tex]
A.
zad. 8
[tex] \frac{ log_{3}(27) }{ log_{3}( \sqrt{27} ) } = \frac{ log_{3}( {3}^{3} ) }{ log_{3}( {3}^{ \frac{3}{2} } ) } = \frac{3}{ \frac{3}{2} } = 2[/tex]
B.
zad. 9
[tex] log_{ \sqrt{7} }(7) = log_{ {7}^{ \frac{1}{2} } }(7) = 2[/tex]
D.
zad. 10
[tex] log_{3}(36) = log_{3}( {6}^{2} ) = 2 log_{3}(6) = 2 log_{3}(3 \times 2) = 2( log_{3}(3) + log_{3}(2) ) = 2(1 + log_{3}(2) ) = 2 + 2 log_{3}(2) [/tex]
odp. C
