[tex]D:5x-10>0 \wedge 3x+1>0\\D:5x>10 \wedge 3x>-1\\D:x>2 \wedge x>-\dfrac{1}{3}\\D:x>2\\\\\log_{50}(5x-10)+\log_{50}(3x+1)=1\\\log_{50}(5x-10)(3x+1)=1\\15x^2+5x-30x-10=50\\15x^2-25x-60=0\\3x^2-5x-12=0\\3x^2-9x+4x-12=0\\3x(x-3)+4(x-3)=0\\(3x+4)(x-3)=0\\x=-\dfrac{4}{3} \vee x=3\\\\-\dfrac{4}{3}\not\in D\\\\\boxed{x=3}[/tex]
