1.

2.
0;\\\\\log^2_3 x-2log_3 x-3=0;\\\\(log_3 x-3)(log_3 x+1)=0;\\\\log_3 x-3;\\\\log_3 x=3;\\\\x=3^3;\\\\x_1=27;\\\\log_3 x+1=0;\\\\log_3 x=-1;\\\\x=3^{-1};\\\\x_2=\frac{1}{3}" alt="log^2_3 x-2log_3 x=3;\\\\x>0;\\\\\log^2_3 x-2log_3 x-3=0;\\\\(log_3 x-3)(log_3 x+1)=0;\\\\log_3 x-3;\\\\log_3 x=3;\\\\x=3^3;\\\\x_1=27;\\\\log_3 x+1=0;\\\\log_3 x=-1;\\\\x=3^{-1};\\\\x_2=\frac{1}{3}" align="absmiddle" class="latex-formula">
0; x>0;\\\\x>0;\\\\lg (x+1.5)+lg x=0;\\\\lg (x+1.5)x=0;\\\\lg (x^2+1.5x)=0;\\\\x^2+1.5x=10^0;\\\\x^2+1.5x-1=0;\\\\(x+2)(x-0.5)=0;\\\\x_1=-2<0;\\\\x_2=0.5;\\\\x=0.5" alt="lg(x+1.5)=-lg x;\\\\x+1.5>0; x>0;\\\\x>0;\\\\lg (x+1.5)+lg x=0;\\\\lg (x+1.5)x=0;\\\\lg (x^2+1.5x)=0;\\\\x^2+1.5x=10^0;\\\\x^2+1.5x-1=0;\\\\(x+2)(x-0.5)=0;\\\\x_1=-2<0;\\\\x_2=0.5;\\\\x=0.5" align="absmiddle" class="latex-formula">
3.
-1;\\\\2x-5>0;\\\\x>2.5;\\\\-log_4 (2x-5)>-1;\\\\log_4 (2x-5)<1;\\\\log_4 (2x-5)<log_4 4;\\\\4>1;\\\\2x-5<4;\\\\2x<4+5;\\\\2x<9;\\\\x<4.5" alt="log_{\frac{1}{4}} (2x-5)>-1;\\\\2x-5>0;\\\\x>2.5;\\\\-log_4 (2x-5)>-1;\\\\log_4 (2x-5)<1;\\\\log_4 (2x-5)<log_4 4;\\\\4>1;\\\\2x-5<4;\\\\2x<4+5;\\\\2x<9;\\\\x<4.5" align="absmiddle" class="latex-formula">