Question 1080342
Let {{{u=9^x}}}, then
{{{u^2=81u+3}}}
{{{u^2-81u=3}}}
{{{u^2-81u+(81/2)^2=3+(81/2)^2}}}
{{{(u-81/2)^2=12/4+6561/4}}}
{{{(u-81/2)^2=6573/4}}}
{{{u-81/2=0 +- sqrt(6573)/2}}}
{{{u=81/2 +- sqrt(6573)/2}}}
{{{9^x=81/2 +- sqrt(6573)/2}}}
Only positive solutions make sense here,
{{{9^x=81/2 + sqrt(6573)/2}}}
{{{x=log(9,(81/2 + sqrt(6573)/2))}}}
{{{highlight(x=log((81/2 + sqrt(6573)/2))/log((9)))}}}