Odpowiedź:
a)2-log₂5=log₂2²-log₂5=log₂4-log₂5=[tex]log_{2}\frac{4}{5}[/tex]
b)[tex]log_{3}\frac{1}{4} -4log_{3}2-3=log_{3}\frac{1}{4} -log_{3}}2^4-log_{3}3^3=log_{3}\frac{\frac{1}{4} }{16} -log_{3}27=log_{3}\frac{1}{4} *\frac{1}{16} -log_{3}27=log_{3}\frac{\frac{1}{64} }{27} =log_{3}\frac{1}{64} *\frac{1}{27}=log_{3}\frac{1}{1762}[/tex]
log₂5=a log₂3=b
a)log₂15=log₂(5*3)=log₂5+log₂3=a+b
b)[tex]log_{2}\frac{5}{9} =log_{2}5-log_{2}9=a-log_{2}3^2=a-2b[/tex]
c)[tex]log_{2}75=log_{2}(25*3)=log_{2}5^2+log_{2}3=2log_{2}5+log_{3}=2a+b[/tex]
d)[tex]log_{2}\frac{1}{27} =log_{2}1-log_{2}27=0-log_{2}3^3=-3log_{3}3=-3b[/tex]
Szczegółowe wyjaśnienie:
