1) ОДЗ:
7; x\neq 8" alt="x>7; x\neq 8" align="absmiddle" class="latex-formula">
![\lg{(\sqrt{2x-3}+2)}=3\lg{\sqrt[3]{x-7}} \lg{(\sqrt{2x-3}+2)}=3\lg{\sqrt[3]{x-7}}](https://tex.z-dn.net/?f=%5Clg%7B%28%5Csqrt%7B2x-3%7D%2B2%29%7D%3D3%5Clg%7B%5Csqrt%5B3%5D%7Bx-7%7D%7D)
![\lg{(\sqrt{2x-3}+2)}=\lg{(x-7)} \lg{(\sqrt{2x-3}+2)}=\lg{(x-7)}](https://tex.z-dn.net/?f=%5Clg%7B%28%5Csqrt%7B2x-3%7D%2B2%29%7D%3D%5Clg%7B%28x-7%29%7D)
![\sqrt{2x-3}=x-7-2 \sqrt{2x-3}=x-7-2](https://tex.z-dn.net/?f=%5Csqrt%7B2x-3%7D%3Dx-7-2)
![\left \{ {{2x-3=(x-9)^2} \atop {x \geq 9}} \right. \left \{ {{2x-3=(x-9)^2} \atop {x \geq 9}} \right.](https://tex.z-dn.net/?f=%5Cleft+%5C%7B+%7B%7B2x-3%3D%28x-9%29%5E2%7D+%5Catop+%7Bx+%5Cgeq+9%7D%7D+%5Cright.)
Из 1-го уравнения корни
. Удовлетворяет только ![x=14 x=14](https://tex.z-dn.net/?f=x%3D14)
Ответ: 14
2) ОДЗ:
-10, x \neq 0" alt="x>-10, x \neq 0" align="absmiddle" class="latex-formula">
![\lg{(|x|(x+10))}=\lg{24} \lg{(|x|(x+10))}=\lg{24}](https://tex.z-dn.net/?f=%5Clg%7B%28%7Cx%7C%28x%2B10%29%29%7D%3D%5Clg%7B24%7D)
![|x|(x+10)=24 |x|(x+10)=24](https://tex.z-dn.net/?f=%7Cx%7C%28x%2B10%29%3D24)
Тут корни
. Они все удовлетворяют ОДЗ
Ответ: -6; -4; 2