Question 149961
{{{2*log(3,(9x))=8}}} Start with the given equation.



{{{log(3,((9x)^2))=8}}} Rewrite the left side using the identity  {{{y*log(b,(x))=log(b,(x^y))}}}



{{{log(3,(81x^2))=8}}} Square {{{9x}}} to get {{{81x^2}}}




{{{3^8=81x^2}}} Rewrite the equation using the property: {{{log(b,(x))=y}}} ====> {{{b^y=x}}}




{{{3^8=3^4x^2}}} Rewrite {{{81}}} as {{{3^4}}}



{{{3^8/3^4=x^2}}} Divide both sides by {{{3^4}}}.



{{{3^(8-4)=x^2}}} Divide the terms on the left side by subtracting the exponents.



{{{3^(4)=x^2}}} Subtract



{{{81=x^2}}} Raise 3 to the 4th power to get 81



{{{0+-sqrt(81)=x}}} Take the square root of both sides.



{{{x=9}}} or {{{x=-9}}} Take the square root of {{{81}}} to get {{{9}}} or {{{-9}}}



Since you <font size=4><b>cannot</b></font> take the log of negative number, this means that we must disregard the possible solution {{{x=-9}}}






So the only solution is {{{x=9}}}