Решить 8 любых примеров кроме
1)а
2)а
3)а

I. б) $16^{frac{3}{4}cdot log_{2}3}=16^{3 cdot frac{1}{4} log_{2}3}=16^{3 log_{2^{4}}3}=16^{3 log_{16}3}=16^{ log_{16}3^{3}}=3^{3}=27$

II. б) $11^{x^{2}+3x}=11^{0}; x^{2}+3x=0; x cdot (x+3)=0; x_{1}=0; x_{2}=-3$

II. в) $36^{x}-5 cdot 6^{x}-6=0; 6^{2x}-5 cdot 6^{x}-6=0; t=6^{x} (t textgreater 0) t^{2}-5t-6=0; t_{1, 2}=frac{5 pm sqrt{25+24}}{2}= frac{5 pm 7}{2}; t_{1}=6 t_{2}=-1 6^{x}=6; x=1$

II. г) $3^{2x+1}-2 cdot 3^{2x-2}=75; 3^{2x} cdot 3- 2 cdot frac{3^{2x}}{9}=75; t=3^{2x} (t textgreater 0) 3t-frac{2}{9}t=75; frac{25}{9}t=75; t=27 3^{2x}=27; 3^{2x}=3^{3} 2x=3; x=frac{3}{2}$

III. б) ОДЗ: $5x-6 textgreater 0; x textgreater frac{6}{5}$ $log_{frac{1}{7}}(5x-6)=-2; -log_{7}(5x-6)=-2; log_{7}(5x-6)=2 log_{7}(5x-6)=log_{7}49; 5x-6=49; 5x=55; x=11$

III. в) ОДЗ: $x^{2}+5x-5 textgreater 0$ $log_{3}(x^2+5x-5)=2; log_{3}(x^2+5x-5)=log_{3}9; x^{2}+5x-5=9; x^{2}+5x-14=0 x_{1, 2}=frac{-5 pm sqrt{25+56}}{2}= frac{-5 pm 9}{2}; x_{1}=2; x_{2}=-7$

III. г) $log^{2}_{3}x + log_{3}x -6=0; t= log_{3}x (x textgreater 0) t^{2}+t-6=0; t_{1, 2}=frac{-1 pm sqrt{1 +24}}{2}= frac{-1 pm 5}{2}; t_{1}=2; t_{2}=-3 log_{3}x=2; log_{3}=-3 x_{1}=9; x_{2}=frac{1}{27}$

I. в) $sqrt{3} cdot ctg(180^{o}+30^{o}) +24 cdot sin{(90^{o}+60^{o})}=sqrt{3} cdotsqrt{3} + 24 cdot frac{1}{2}==3+12=15$