Question 882278
{{{log((x-9))=1-log((x))}}}



{{{log((x-9))+log((x))=1}}}



{{{log((x))+log((x-9))=1}}}



{{{log((x*(x-9)))=1}}}



{{{x*(x-9)=10^1}}}



{{{x*(x-9)=10}}}



{{{x^2-9x=10}}}



{{{x^2-9x-10=0}}}



{{{(x-10)(x+1)=0}}}



{{{x-10=0}}} or {{{x+1=0}}}



{{{x=10}}} or {{{x=-1}}}



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The *possible* solutions are {{{x=10}}} or {{{x=-1}}}



However, the domain of {{{log((x))}}} is {{{x>0}}}



So {{{x=-1}}} is NOT possible as it's NOT in the domain of {{{log((x))}}}



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The only solution is {{{x=10}}}