Question

ALGUIEN SABE COMO HALLAR LA SIUENTE FUNCION LOGARITMICA LOG3(2X-1)-LOG3(5X+2)=LOG3(X-2)-2

Answer 1

$<var>\\\log_3(2x-1)-\log_3(5x+2)=\log_3(x-2)-2\\ D:2x-1>0 \wedge 5x+2>0 \wedge x-2>0\\ D:2x>1 \wedge 5x>-2 \wedge x>2\\ D:x>\frac{1}{2} \wedge x>-\frac{2}{5} \wedge x>2\\ D:x>2\\ \log_3(2x-1)+2=\log_3(x-2)+\log_3(5x+2)\\ \log_3(2x-1)+\log_39=\log_3(x-2)(5x+2)\\ \log_39(2x-1)=\log_3(x-2)(5x+2)\\ 18x-9=5x^2+2x-10x-4\\ 5x^2-26x+5=0\\\\ </var>$

$<var>\\\\\Delta=(-26)^2-4\cdot5\cdot5\\ \Delta=676-100\\ \Delta=576\\ \sqrt{\Delta}=24\\\\ x_1=\frac{-(-26)-24}{2\cdot5}\\ x_1=\frac{2}{10}\\ x_1=\frac{1}{5}\\\\ x_2=\frac{-(-26)+24}{2\cdot5}\\ x_2=\frac{50}{10}\\ x_2=5\\\\ x_1\not\in D\\\\ \underline{x=5}\\ </var>$