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[latex] log_{ \frac{1}{6} } (10-x)+log_{ \frac{1}{6} }(x-3)=-1[/latex] [latex] log_{ \frac{1}{6} } (10-x)(x-3)=-1[/latex] [latex] log_{ \frac{1}{6} } (10-x)(x-3) = log_{ \frac{1}{6} }6[/latex] [latex] (10-x)(x-3) = 6[/latex] [latex]10x-30-x^2+3x=6[/latex] [latex]13x-36-x^2=0[/latex] [latex]D = 13^2-4*(-36)*(-1)=169-144=25[/latex] [latex] x_{1} = \frac{-13+5}{-2} = \frac{8}{2}=4 [/latex] [latex] x_{2}= \frac{-13-5}{-2} = 9 [/latex]