Question

log(1-2x)=log(x+45)-log(-x-3)

Answer 1

$\log(1-2x)=log(x+45)-log(-x-3)\\ 1-2x>0 wedge x+45>0 wedge -x-3 >0\ -2x>-1 wedge x>-45 wedge -x>3\ x<frac{1}{2} wedge x>-45 wedge x<-3\ xin(-45,-3)\\ log(1-2x)=logfrac{x+45}{-x-3}\ 1-2x=frac{x+45}{-x-3}\ (1-2x)(-x-3)=x+45\ -x-3+2x^2+6x=x+45\ 2x^2+4x-48=0\ x^2+2x-24=0\ x^2+6x-4x-24=0\ x(x+6)-4(x+6)=0\ (x-4)(x+6)=0\ x=4 vee x=-6\ 4not in (-45,-3)\\ underline{x=-6}$

Answer 2

решение во вложении

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