![image](https://tex.z-dn.net/?f=log_5%28x%2B3%29%3D1-log_5%28x-1%29%5C%3B+%2C%5C%3B+%5C%3B+ODZ%3A%5C%3B++%5Cleft+%5C%7B+%7B%7Bx%2B3%3E0%7D+%5Catop+%7Bx-1%3E0%7D%7D+%5Cright.+%2C%5C%3B+x%3E1%5C%5C%5C%5Clog%28x%2B3%29%2Blog_5%28x-1%29%3D1%2C%5C%3B+%5C%3B+1%3Dlog_55%5C%5C%5C%5C%28x%2B3%29%28x-1%29%3D5%5C%5C%5C%5Cx%5E2%2B2x-8%3D0%5C%5C%5C%5Cx_1%3D-4%3C1%2C%5C%3B+x_2%3D2%5C%5C%5C%5COtvet%3A%5C%3B+x%3D2.)
0} \atop {x-1>0}} \right. ,\; x>1\\\\log(x+3)+log_5(x-1)=1,\; \; 1=log_55\\\\(x+3)(x-1)=5\\\\x^2+2x-8=0\\\\x_1=-4<1,\; x_2=2\\\\Otvet:\; x=2." alt="log_5(x+3)=1-log_5(x-1)\; ,\; \; ODZ:\; \left \{ {{x+3>0} \atop {x-1>0}} \right. ,\; x>1\\\\log(x+3)+log_5(x-1)=1,\; \; 1=log_55\\\\(x+3)(x-1)=5\\\\x^2+2x-8=0\\\\x_1=-4<1,\; x_2=2\\\\Otvet:\; x=2." align="absmiddle" class="latex-formula">