Verified answer

Ответ: 1) х=2; 2) х=7.

Объяснение:

[tex]\displaystyle\bf\\1)\\\\\log_{5} (x-1)=0\\\\ODZ \ :\\\\x-1 > 0 \ \ \Rightarrow \ \ x > 1\\\\\\x-1=5^\circ \\\\x-1=1\\\\\boxed{x=2}\\\\2)\\\\\lg(x+3)=1\\\\ODZ \ : \\\\x+3 > 0 \ \ \Rightarrow \ \ x > -3\\\\\\x+3=10^{1} \\\\x+3=10\\\\\boxed{x=7}[/tex]