Odpowiedź:
zad. 1
a)
[tex] \frac{ {5}^{3} \times {5}^{4} }{ {5}^{2} \times 5} = \frac{ {5}^{7}}{ {5}^{3} } = {5}^{4} = 625[/tex]
b)
[tex] \sqrt{2} \times \sqrt{128} = \sqrt{2 \times 128} =[/tex]
[tex] = \sqrt{256} = 16[/tex]
c)
[tex] \sqrt[3]{16} \div \sqrt[3]{4} = \sqrt[3]{4} [/tex]
d)
[tex] \frac{log20 + log5}{log_381 \div log_232} = \frac{log100}{4 \div 5} = \frac{2}{0.8} = [/tex]
[tex] \frac{2}{1} \div \frac{4}{5} = \frac{2}{1} \times \frac{5}{4} = \frac{5}{2} = 2.5[/tex]
e)
[tex]log_ \frac{1}{5} 125 = - 3[/tex]
[tex]( { \frac{1}{5})}^{ - 3} = {5}^{3} = 125[/tex]
zad. 2
[tex] \frac{5 \sqrt{3} }{3 + \sqrt{3} } \times \frac{3 - \sqrt{3} }{3 - \sqrt{3} } = \frac{(5 \sqrt{3})(3 - \sqrt{3}) }{(3 + \sqrt{3})(3 - \sqrt{3}) } =[/tex]
[tex] = \frac{15 \sqrt{3} - 15 }{9 - 3} = \frac{3(5 \sqrt{3} - 5)}{6} = \frac{5 \sqrt{3} - 5 }{2} [/tex]
