Odpowiedź:
4.
a)
[tex]3log_{3}\sqrt{2}-\frac{1}{2}log_{3}2-log_{3}6=log_{3}\sqrt{2}^{3}-log_{3}2^{\frac{1}{2}}-log_{3}6=log_{3}(2^{\frac{3}{2}}:2^{\frac{1}{2}}:6)=log_{3}\frac{1}{3}=-1[/tex]
b)
[tex]log_{2}0.08+4log_{2}5-log_{2}12.5=log_{2}0.08+log_{2}5^{4}-log_{2}12.5=log_{2}(0.08*625:12.5)=log_{2}4=2[/tex]
c)
[tex]log_{5}2.4+\frac{2}{3}log_{5}0.125-log_{5}3=log_{5}2.4+log_{5}0.125^{\frac{2}{3}}-log_{5}3=log_{5}(2.4*(\frac{1}{8})^{\frac{2}{3}}:3)=log_{5}\frac{1}{5}=-1[/tex]
d)
[tex]log2.5-\frac{3}{2}log0.25+log50=log2.5-log0.25^\frac{3}{2}+log50=log(2.5:0.25^{\frac{3}{2}}*50)=log1000=3[/tex]
Szczegółowe wyjaśnienie:
