Question 1100499
{{{3^x-1/3^x=4}}}
{{{3^(2x)-1=4*3^(2x)}}}
Use a substitution,
{{{u=3^x}}}
{{{u^2=3^(2x)}}}
So,
{{{u^2-1=4u}}}
{{{u^2-4u-1=0}}}
{{{u^2-4u+4-1=4}}}
{{{(u-2)^2=5}}}
{{{u-2=0 +- sqrt(5)}}}
{{{u=2 +- sqrt(5)}}}
{{{3^x=2 +- sqrt(5)}}}
The negative sign would lead to a negative right hand side which is not a possible solution.
{{{3^x=2+sqrt(5)}}}
{{{x=log(3,(2+sqrt(5)))}}}
{{{highlight(x=log((2+sqrt(5)))/log((3)))}}}