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ОДЗ
![left { {{x-5 textgreater 0} atop {x+2 textgreater 0}} right. \ \ left { {{x textgreater 5} atop {x textgreater -2}} right. \ \ x textgreater 5 left { {{x-5 textgreater 0} atop {x+2 textgreater 0}} right. \ \ left { {{x textgreater 5} atop {x textgreater -2}} right. \ \ x textgreater 5](https://tex.z-dn.net/?f=+left+%7B+%7B%7Bx-5+textgreater++0%7D+atop+%7Bx%2B2+textgreater++0%7D%7D+right.+%5C+%5C+left+%7B+%7B%7Bx+textgreater++5%7D+atop+%7Bx+textgreater++-2%7D%7D+right.+%5C+%5C+x+textgreater++5)
![log_2(x-5)+log_2(x+2) textgreater 3 \ \ log_2(x-5)(x+2) textgreater 3 \ \ (x+2)(x-5) textgreater 2^3 \ \ x^{2} -5x+2x-10 textgreater 8 \ \ x^{2} -3x-18 textgreater 0 \ \ D=3^2+4*18= 81 \ \ x_1= frac{3+9}{2}=6 \ \ x_2=frac{3-9}{2}=-3 \ \ x in (-infty; -3) U (6; + infty) log_2(x-5)+log_2(x+2) textgreater 3 \ \ log_2(x-5)(x+2) textgreater 3 \ \ (x+2)(x-5) textgreater 2^3 \ \ x^{2} -5x+2x-10 textgreater 8 \ \ x^{2} -3x-18 textgreater 0 \ \ D=3^2+4*18= 81 \ \ x_1= frac{3+9}{2}=6 \ \ x_2=frac{3-9}{2}=-3 \ \ x in (-infty; -3) U (6; + infty)](https://tex.z-dn.net/?f=log_2%28x-5%29%2Blog_2%28x%2B2%29+textgreater++3+%5C+%5C+log_2%28x-5%29%28x%2B2%29+textgreater++3+%5C+%5C+%28x%2B2%29%28x-5%29+textgreater++2%5E3+%5C+%5C+x%5E%7B2%7D+-5x%2B2x-10+textgreater++8+%5C+%5C+x%5E%7B2%7D+-3x-18+textgreater++0+%5C+%5C+D%3D3%5E2%2B4%2A18%3D+81+%5C+%5C+x_1%3D+frac%7B3%2B9%7D%7B2%7D%3D6+%5C+%5C+x_2%3Dfrac%7B3-9%7D%7B2%7D%3D-3+%5C++%5C+x+in+%28-infty%3B+-3%29+U+%286%3B+%2B+infty%29)
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Ответ х ∈ (6; +∞)
Объединим с ОДЗ
х ∈ (6; +∞)
Ответ х ∈ (6; +∞)
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