[tex]~~~~~~~~~~~~log_{3} x-log_{3} y=log_{3} \frac{x}{y} \\\\a)~~x=27,~~y=9\\\\L=log_{3} 27-log_{3} 9=log_{3} 3^{3} -log_{3} 3^{2} =3log_{3} 3-2log_{3} 3=3\cdot 1 - 2\cdot 1=3-2=1\\\\P=log_{3} \frac{27}{9}=log_{3} 3=1\\\\L=P~~~~cbdu.\\\\b)~~x=81,~~y=9\\\\L=log_{3} 81-log_{3} 9=log_{3} 3^{4} -log_{3} 3^{2} =4log_{3} 3-2log_{3} 3=4\cdot 1-2\cdot 1=4-2=2\\\\P=log_{3} \frac{81}{9}=log_{3} 9=log_{3} 3^{2} =2log_{3} 3=2\cdot 1 =2\\\\L=P~~~~~cbdu.\\\\c)~~x=3,~~y=\sqrt{3} \\\\[/tex]
[tex]L=log_{3}3 -log_{3} \sqrt{3} =1-log_{3}3^{\frac{1}{2} } =1-\frac{1}{2} log_{3} 3=1-\frac{1}{2} \cdot 1=1-\frac{1}{2} =\dfrac{1}{2} \\\\P=log_{3} \dfrac{3}{\sqrt{3} } =log_{3}\dfrac{3^{1} }{3^{\frac{1}{2} } } =log_{3}3^{1-\frac{1}{2} } =log_{3}3^{\frac{1}{2} } =\dfrac{1}{2} log_{3}3=\dfrac{1}{2} \cdot 1 =\dfrac{1}{2} \\\\L=P~~~~cbdu.\\\\korzystam~~ze~~wzoru:~~log_{a} a=1[/tex]
