Odpowiedź:
[tex]log_512=a\quad log_52=b\\\\log_56=log_5(\frac{12}{2} )=log_512-log_52=a-b\\log_59=log_5(\frac{144}{16} )=log_5144-log_516=log_512^{2} -log_52^4=\\=2log_512-4log_52=2a-4b[/tex]
[tex]log_512=log_5(4\cdot3)=lo_54+log_53=log_52^2+log_53=2log_52+log_53\\a=2b+log_53\Rightarrow log_53=a-2b\\\\log_5\sqrt[5]{3} =log_53^{\frac{1}{5} }=\frac{1}{5} log_53=\frac{1}{5} (a-2b)\\log_350=\frac{log_550}{log_53} \\log_550=log_5(5^2\cdot2)=log_55^2+log_52=2+log_52=2+b\\log_350=\frac{log_550}{log_53} =\frac{2+b}{a-2b}[/tex]
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Odpowiedź:
[tex]log_512=a\quad log_52=b\\\\log_56=log_5(\frac{12}{2} )=log_512-log_52=a-b\\log_59=log_5(\frac{144}{16} )=log_5144-log_516=log_512^{2} -log_52^4=\\=2log_512-4log_52=2a-4b[/tex]
[tex]log_512=log_5(4\cdot3)=lo_54+log_53=log_52^2+log_53=2log_52+log_53\\a=2b+log_53\Rightarrow log_53=a-2b\\\\log_5\sqrt[5]{3} =log_53^{\frac{1}{5} }=\frac{1}{5} log_53=\frac{1}{5} (a-2b)\\log_350=\frac{log_550}{log_53} \\log_550=log_5(5^2\cdot2)=log_55^2+log_52=2+log_52=2+b\\log_350=\frac{log_550}{log_53} =\frac{2+b}{a-2b}[/tex]