Answer
$x=-\dfrac{3}{2}$
Work Step by Step
$\dfrac{1}{27}=3^{2x}$
Rewrite $27$ as $3^{3}$:
$\dfrac{1}{3^{3}}=3^{2x}$
Take $3^{3}$ to the numerator by changing the sign of its exponent:
$3^{-3}=3^{2x}$
If $3^{-3}=3^{2x}$, then $2x=-3$
$2x=-3$
Solve for $x$:
$x=-\dfrac{3}{2}$
