Question

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

Answer 1

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

Answer 2

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