Zadanie 1
a)
log_23*log_35*log_58=log_25*log_58=log_28=log_22^3=3
b)
36log_2\sqrt[4]{2\sqrt[3]{2}}=36log_22^{\frac{1}{4}}*2^{\frac{1}{12}}=36log_2(2^{\frac{3+1}{12}})=log_2(2^{\frac{1}{3}})^{36}=log_22^{12}=12
c)
2^{log7}*5^{log7}=(2*5)^{log7+log7}=10^{2log7}
d)
log_{27}(log_8\sqrt[5]{32})=log_{27}(log_8\sqrt[5]{2^5})=log_{27}(log_82)=log_{27}(log_8\sqrt[3]8)=
=log_{27}(log_88^{\frac{1}{3}})=log_{27}\frac{1}{3}=log_{27}3^{-1}=log_{27}(\sqrt[3]{27})^{-1}=log_{27}(27^{\frac{1}{3}})^{-1}=log_{27}27^{-\frac{1}{3}}=-\frac{1}{3}
e)
log_36*log_67*log_79=log_37*log_79=log_39=log_33^2=2
log
---------
log_ab*log_bc=log_ac wzór