Zad. na nudę:
6.
a) Porównaj liczby:
![a=( \sqrt[4]{125} )^{^6](https://tex.z-dn.net/?f=a%3D%28+%5Csqrt%5B4%5D%7B125%7D+%29%5E%7B%5E6 "a=( \sqrt[4]{125} )^{^6")
b) Oblicz:
6.
a) Porównaj liczby:
b) Oblicz:
jestemt
![a = (\sqrt[4]{125})^6 = (\sqrt[4]{5^3})^6 = (5^\frac34)^6 = 5^{\frac34*6} = 5^{\frac92}\\\\b = (5\sqrt5)^3 = (5*5^{\frac12})^3 = (5^{1+\frac12})^3 = 5^{\frac32*3} = 5^\frac92\\\\a = b](https://tex.z-dn.net/?f=a+%3D+%28%5Csqrt%5B4%5D%7B125%7D%29%5E6+%3D+%28%5Csqrt%5B4%5D%7B5%5E3%7D%29%5E6+%3D+%285%5E%5Cfrac34%29%5E6+%3D+5%5E%7B%5Cfrac34%2A6%7D+%3D+5%5E%7B%5Cfrac92%7D%5C%5C%5C%5Cb+%3D+%285%5Csqrt5%29%5E3+%3D+%285%2A5%5E%7B%5Cfrac12%7D%29%5E3+%3D+%285%5E%7B1%2B%5Cfrac12%7D%29%5E3+%3D+5%5E%7B%5Cfrac32%2A3%7D+%3D+5%5E%5Cfrac92%5C%5C%5C%5Ca+%3D+b "a = (\sqrt[4]{125})^6 = (\sqrt[4]{5^3})^6 = (5^\frac34)^6 = 5^{\frac34*6} = 5^{\frac92}\\\\b = (5\sqrt5)^3 = (5*5^{\frac12})^3 = (5^{1+\frac12})^3 = 5^{\frac32*3} = 5^\frac92\\\\a = b")
![b) \\log_415+2log_8\sqrt{125} = log_415+log_8(\sqrt{125})^2 = log_415+log_8125=\\\\=\frac{log_215}{log_24}+\frac{log_2125}{log_28} = \frac{log_215}{log_22^2}+\frac{log_2125}{log_22^3} = \frac{log_215}{2}+\frac{log_2125}{3} =\\\\= \frac12log_215+\frac13log_2125 = log_2\sqrt{15}+log_2\sqrt[3]{125} = log_2\sqrt{15}+log_25 = \\\\log_2\sqrt{15}*5 = log_2\sqrt{15*25} = log_2\sqrt{375}= \frac12log_2375 =\\\\= \frac12*\frac{log375}{log2}\approx4,28](https://tex.z-dn.net/?f=b%29+%5C%5Clog_415%2B2log_8%5Csqrt%7B125%7D+%3D+log_415%2Blog_8%28%5Csqrt%7B125%7D%29%5E2+%3D+log_415%2Blog_8125%3D%5C%5C%5C%5C%3D%5Cfrac%7Blog_215%7D%7Blog_24%7D%2B%5Cfrac%7Blog_2125%7D%7Blog_28%7D+%3D+%5Cfrac%7Blog_215%7D%7Blog_22%5E2%7D%2B%5Cfrac%7Blog_2125%7D%7Blog_22%5E3%7D+%3D+%5Cfrac%7Blog_215%7D%7B2%7D%2B%5Cfrac%7Blog_2125%7D%7B3%7D+%3D%5C%5C%5C%5C%3D+%5Cfrac12log_215%2B%5Cfrac13log_2125+%3D+log_2%5Csqrt%7B15%7D%2Blog_2%5Csqrt%5B3%5D%7B125%7D+%3D+log_2%5Csqrt%7B15%7D%2Blog_25+%3D+%5C%5C%5C%5Clog_2%5Csqrt%7B15%7D%2A5+%3D+log_2%5Csqrt%7B15%2A25%7D+%3D+log_2%5Csqrt%7B375%7D%3D+%5Cfrac12log_2375+%3D%5C%5C%5C%5C%3D+%5Cfrac12%2A%5Cfrac%7Blog375%7D%7Blog2%7D%5Capprox4%2C28 "b) \\log_415+2log_8\sqrt{125} = log_415+log_8(\sqrt{125})^2 = log_415+log_8125=\\\\=\frac{log_215}{log_24}+\frac{log_2125}{log_28} = \frac{log_215}{log_22^2}+\frac{log_2125}{log_22^3} = \frac{log_215}{2}+\frac{log_2125}{3} =\\\\= \frac12log_215+\frac13log_2125 = log_2\sqrt{15}+log_2\sqrt[3]{125} = log_2\sqrt{15}+log_25 = \\\\log_2\sqrt{15}*5 = log_2\sqrt{15*25} = log_2\sqrt{375}= \frac12log_2375 =\\\\= \frac12*\frac{log375}{log2}\approx4,28")
2 votes
Thanks 1
More Questions From This User See All
Recommend Questions
ola737626
October 2020 | 0 Replies
BŁAGAM POMÓŻCIE PLIIIISSSSSSSS ❤️❤️❤️ DAJE ❤️ I NAJ!!!!!! BĘDĘ WDZIĘCZNA PLISSSSSSSSS...W tabeli (w załączniku) podano wyniki zakończonego sezonu szkolnej ligi piłkarskiej każda z drużyn rozegrała 10 meczów. Za wygrany mecz otrzymywała 3 punkty za remis 1 punkt a za porażkę 0 punktówWykonaj polecenie i napisz działanie Niebiescy w 10 meczach zdobyli 26 punktów. Ile razy odnieśli zwycięstwo A ile razy zremisowali