МОДЕРАТОР найдешь ошибку, прими за улыбку *)
0; 4x-3>0;\\ log_5 (4x+19)=log_5 (4x-3)+log_5 5;\\ log_5 (4x+19)=log_5 5(4x-3);\\ 4x+19=5(4x-3);\\ 4x+19=20x-15;\\ 20x-4x=19+15; 16x=34; 8x=17; x=\frac{17}{8}=2.125" alt="1) log_5 (4x+19)=log_5 (4x-3)+1;\\ 4x+19>0; 4x-3>0;\\ log_5 (4x+19)=log_5 (4x-3)+log_5 5;\\ log_5 (4x+19)=log_5 5(4x-3);\\ 4x+19=5(4x-3);\\ 4x+19=20x-15;\\ 20x-4x=19+15; 16x=34; 8x=17; x=\frac{17}{8}=2.125" align="absmiddle" class="latex-formula">
1" alt="2) log_3 (3+\sqrt{x})+log_3(1+x^2)=0;\\ log_3 (3+\sqrt{x})(1+x^2)=0;\\ (3+\sqrt{x})(1+x^2)=3^0;\\ (3+\sqrt{x})(1+x^2)=1;\\ 3+\sqrt{x} \geq 3;\\ 1+x^2 \geq 1; (3+\sqrt{x})(1+x^2) \geq 3*1=3 >1" align="absmiddle" class="latex-formula">
решений нет
0;\\ (2+log_2 x)^2-(1+log_2 x)^2+log_2 x=9;\\ log^2_2 x+4log_2 x+4-log^2_2 x-2log_2 x-1+log_2 x-9=0;\\ 3log_2 x-6=0;\\ log_2 x=2;\\ x=2^2=4;" alt="3) log^2_2(4x)-log^2_2 (2x)+log_2 x=9; \\ x>0;\\ (2+log_2 x)^2-(1+log_2 x)^2+log_2 x=9;\\ log^2_2 x+4log_2 x+4-log^2_2 x-2log_2 x-1+log_2 x-9=0;\\ 3log_2 x-6=0;\\ log_2 x=2;\\ x=2^2=4;" align="absmiddle" class="latex-formula">
0; x+3 \neq 0; x+1 \neq 0;\\ log_3 (x^2-3)^2=log_3 (x+3)^2(x+1)^2;\\ (x^2-3)^2=(x+3)^2(x+1)^2;\\ (x^2-3)^2=(x+3)^2(x+1)^2;\\ (x^2-3)^2=((x+3)(x+1))^2;\\ (x^2-3)^2=(x^2+4x+3)^2;\\ /1. x^2-3=x^2+4x+3;\\ 4x+3=-3;\\ 4x=-6;\\ x_1=-1.5;\\ /2. x^2-3=-x^2-4x-3;\\ 2x^2+4x=0;\\ x^2+2x=0;\\ x_2=0;\\ x_3=-2;\\ x=-2" alt="4) 2log_3 (x^2-3)=log_3 (x+3)^2+log_3 (x+1)^2;\\ x^2-3>0; x+3 \neq 0; x+1 \neq 0;\\ log_3 (x^2-3)^2=log_3 (x+3)^2(x+1)^2;\\ (x^2-3)^2=(x+3)^2(x+1)^2;\\ (x^2-3)^2=(x+3)^2(x+1)^2;\\ (x^2-3)^2=((x+3)(x+1))^2;\\ (x^2-3)^2=(x^2+4x+3)^2;\\ /1. x^2-3=x^2+4x+3;\\ 4x+3=-3;\\ 4x=-6;\\ x_1=-1.5;\\ /2. x^2-3=-x^2-4x-3;\\ 2x^2+4x=0;\\ x^2+2x=0;\\ x_2=0;\\ x_3=-2;\\ x=-2" align="absmiddle" class="latex-formula">
0;\\ \frac{1}{x}-2=4^1;\\ \frac{1}{x}-2=4;\\ \frac{1}{x}=6;\\ x=\frac{1}{6} " alt="5) log_4 (x^{-1}-2)=1;\\ x \neq 0; \frac{1}{x}-2>0;\\ \frac{1}{x}-2=4^1;\\ \frac{1}{x}-2=4;\\ \frac{1}{x}=6;\\ x=\frac{1}{6} " align="absmiddle" class="latex-formula">
0; 1.5x+1>0;\\ lg(x-1)^2=lg(1.5x+1);\\ (x-1)^2=1.5x+1;\\ x^2-2x+1=1.5x+1;\\ x^2-3.5x=0;\\ x_1=0;\\ x_2=3.5;\\ x=3.5 " alt="6) 2lg (x-1)=lg(1.5x+1); \\ x-1>0; 1.5x+1>0;\\ lg(x-1)^2=lg(1.5x+1);\\ (x-1)^2=1.5x+1;\\ x^2-2x+1=1.5x+1;\\ x^2-3.5x=0;\\ x_1=0;\\ x_2=3.5;\\ x=3.5 " align="absmiddle" class="latex-formula">
0; x+2\ neq 1; 3x^2-12>0;\\ 3x^2-12=(x+2)^2;\\ 3x^2-12=x^2+4x+4;\\ 2x^2-4x-16=0;\\ x^2-2x-8=0;\\ (x-4)(x+2)=0;\\ x_1=4;\\ x_2=-2;\\ " alt="7) log{x+2} (3x^2-12)=2; x+2>0; x+2\ neq 1; 3x^2-12>0;\\ 3x^2-12=(x+2)^2;\\ 3x^2-12=x^2+4x+4;\\ 2x^2-4x-16=0;\\ x^2-2x-8=0;\\ (x-4)(x+2)=0;\\ x_1=4;\\ x_2=-2;\\ " align="absmiddle" class="latex-formula">
решений нет
0;\\ 0.5log_3 x*(1+log_3 x)=1;\\ log^2_3 x+log_3 x-2=0;\\ (log_3 x+2)(log_3 x-1)=0;\\ /1. log_3 x=-2;\\ x_1=3^{-2}=\frac{1}{9};\\ /2. log_3 x=1;\\ x_2=3^1=3;\\" alt="8) log_3 x *log_9 (3x)=2log_9 3;\\ x>0;\\ 0.5log_3 x*(1+log_3 x)=1;\\ log^2_3 x+log_3 x-2=0;\\ (log_3 x+2)(log_3 x-1)=0;\\ /1. log_3 x=-2;\\ x_1=3^{-2}=\frac{1}{9};\\ /2. log_3 x=1;\\ x_2=3^1=3;\\" align="absmiddle" class="latex-formula">
0;\\ 2^x=4;\\ 2^x=2^2;\\ x=2" alt="9) log_3 (2^x-1)+log_3 (2^x-3)=1;\\ log_3 ((2^x-1)(2^x-3))=1;\\ (2^x-1)(2^x-3)=3^1;\\ (2^x)^2-4*2^x+3=3;\\ (2^x)^2-4*2^x=0;\\ 2^x>0;\\ 2^x=4;\\ 2^x=2^2;\\ x=2" align="absmiddle" class="latex-formula">