Answer
$x=4$
Work Step by Step
RECALL:
(i) If $a^M=a^N$, then $M=N.$
(ii) $(a^m)^n=a^{mn}.$
Note that $\dfrac{1}{27}=\dfrac{1}{3^3} = 3^{-3}$.
Thus, the given equation can be written as
$3^{1-x} = 3^{-3}.$
Use rule (i) above to obtain
$1-x=-3
\\-x = -3-1
\\-x=-4
\\(-1)(-x)=-4(-1)
\\x=4.$
