Задача 4

[Гост]

log 7 (x 2 – 2x – 8 )= 1

[ammornil]

log 7 (x 2 – 2x – 8 )= 1

[tex]log_{7}(x^{2}-2x-8)=1[/tex]

[tex]DM: x^{2}-2x-8>0, D=1^{2}+1.8=9, x_{_{1,2}}=\frac{1\pm3}{1} \Rightarrow (x-4)(x+2)>0 \Leftrightarrow x \in (- \infty;-2) \cup (4;+ \infty)[/tex]

[tex]log_{7}(x^{2}-2x-8)=log_{7}7^{1} \Leftrightarrow x^{2}-2x-8=1 \Leftrightarrow x^{2}-2x-9=0[/tex]
[tex]D=1^{2}+1.9=10 \rightarrow x_{_{1,2}}=\frac{1\pm\sqrt{10}}{1} \begin{cases} x_{_{1}}=1-\sqrt{10} <-2 \Rightarrow x_{1} \in DM \\ x_{_{2}}=1+\sqrt{10} >4 \Rightarrow x_{2} \in DM \end{cases}[/tex]

[tex][/tex]