Question

lg^2x=4-3lgx

lg(x-2)+lg(x-3)=1-lg5

Answer 1

$\x>0\\ lg^2x=4-3lg x\ lg^2x+3lg x-4=0\ lg^2x-lg x+4lg x-4=0\ lg x(lg x-1)+4(lg x-1)=0\ (lg x +4)(lg x-1)=0\ lg x+4=0 vee lg x -1=0\ lg x=-4 vee lg x=1\ x=10^{-4} vee x=10^1\ x=frac{1}{10000} vee x=10$

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$\x-2 >0 wedge x-3>0\ x>2 wedge x>3\ x>3\\ lg(x-2)+lg(x-3)=1-lg 5\ lg(x-2)(x-3)=lg 10-lg 5\ lg(x^2-3x-2x+6)=lg frac{10}{5}\ lg(x^2-5x+6)=lg 2\ x^2-5x+6=2\ x^2-5x+4=0\ x^2-x-4x+4=0\ x(x-1)-4(x-1)=0\ (x-4)(x-1)=0\ x=4 vee x=1\\ 1not>3Rightarrow x=4$