0 \wedge x+45>0 \wedge -x-3 >0\\ -2x>-1 \wedge x>-45 \wedge -x>3\\ x<\frac{1}{2} \wedge x>-45 \wedge x<-3\\ x\in(-45,-3)\\\\ \log(1-2x)=\log\frac{x+45}{-x-3}\\ 1-2x=\frac{x+45}{-x-3}\\ (1-2x)(-x-3)=x+45\\ -x-3+2x^2+6x=x+45\\ 2x^2+4x-48=0\\ x^2+2x-24=0\\ x^2+6x-4x-24=0\\ x(x+6)-4(x+6)=0\\ (x-4)(x+6)=0\\ x=4 \vee x=-6\\ 4\not \in (-45,-3)\\\\ \underline{x=-6} " alt="\\\log(1-2x)=\log(x+45)-\log(-x-3)\\\\ 1-2x>0 \wedge x+45>0 \wedge -x-3 >0\\ -2x>-1 \wedge x>-45 \wedge -x>3\\ x<\frac{1}{2} \wedge x>-45 \wedge x<-3\\ x\in(-45,-3)\\\\ \log(1-2x)=\log\frac{x+45}{-x-3}\\ 1-2x=\frac{x+45}{-x-3}\\ (1-2x)(-x-3)=x+45\\ -x-3+2x^2+6x=x+45\\ 2x^2+4x-48=0\\ x^2+2x-24=0\\ x^2+6x-4x-24=0\\ x(x+6)-4(x+6)=0\\ (x-4)(x+6)=0\\ x=4 \vee x=-6\\ 4\not \in (-45,-3)\\\\ \underline{x=-6} " align="absmiddle" class="latex-formula">