Question 798863
{{{f(x)=log(10,(1-log(10,(x^2-5x+16))))}}}
Logarithms are only defined for positive numbers, so {{{f(x)}}} exists only when
{{{1-log(10,(x^2-5x+16))>0}}} and {{{x^2-5x+16>0}}}
Luckily, {{{x^2-5x+16>0}}} for all real values of {{{x}}}.
 
{{{1-log(10,(x^2-5x+16))>0}}} <--> {{{1>log(10,(x^2-5x+16))}}} <--> {{{10>x^2-5x+16}}} <--> {{{0>x^2-5x+16-10}}} <--> {{{0>x^2-5x+6}}} <--> {{{0>(x-3)(x-2)}}} <--> {{{highlight(2<x<3 )}}}