Question 373563
Note that {{{1/81 = 1/(3^4)}}}
{{{1/(3^4) = 3^(-4)}}}
So, now I can write
{{{3^(x^2 + 5x) = 3(-4)}}}
{{{x^2 + 5x = -4}}}
Solve by completing square
{{{x^2 + 5x + (5/2)^2 = -4 + (5/2)^2}}}
{{{(x + 5/2)^2 = 25/4 - 16/4}}}
{{{(x + 5/2)^2 = (3/2)^2}}}
{{{x + 5/2 = 3/2}}}
{{{x = - 1}}}
and also
{{{x + 5/2 = -3/2}}}
{{{x = -4}}}
check the answers:
{{{3^(x^2+5x) = 1/81}}}
{{{3^(1 + 5*(-1)) = 1/81}}}
{{{3^(-4) = 3^(-4)}}}
OK
and also
{{{3^((-4)^2 + 5*(-4)) = 1/81}}}
{{{3^(16 - 20) = 3^(-4)}}}
{{{3^(-4) = 3^(-4)}}}
OK