Question 193107
{{{19^(1-x)= 12}}} Start with the given equation.



{{{log(10,(19^(1-x)))= log(10,(12))}}} Take the log base 10 of both sides



{{{(1-x)log(10,(19))= log(10,(12))}}} Pull down the exponent



{{{1-x=log(10,(12))/log(10,(19))}}} Divide both sides by {{{log(10,(19))}}}.



{{{1-x=log(19,(12))}}} Use the change of base formula to rewrite the right side



{{{-x=log(19,(12))-1}}} Subtract 1 from both sides.



{{{x=-log(19,(12))+1}}} Multiply EVERY term by -1 to isolate "x"



So the solution is {{{x=-log(19,(12))+1}}} which approximates to *[Tex \LARGE x \approx 0.15607]