Question 853665
{{{(sqrt(3))^(x+2)/27^x=3^(-x^2) }}}
= {{{(sqrt(3))^(x+2)/sqrt(3)^(6x) = 3^(-x^2) }}}
= {{{(sqrt(3))^(x+2)/sqrt(3)^(6x) = sqrt(3)^(-2x^2) }}}
= {{{(sqrt(3))^(-5x+2) = sqrt(3)^(-2x^2) }}}
{{{-5x + 2 = -2x^2}}}
{{{2x^2 - 5x + 2 = 0}}}
(2x - 1)*(x - 2) = 0
x = 1/2
x = 2
You can check both answers.