Answer
$x=4$
Work Step by Step
We are given the exponential equation $3^{1-x}=\frac{1}{27}$.
We can express each side using a common base and then solve for $x$.
$3^{1-x}=3^{-3}=\frac{1}{3^{3}}\frac{1}{27}$
Take the natural log of both sides.
$ln(3^{1-x})=ln(3^{-3})$
$(1-x)ln(3)=-3ln(3)$
Divide both sides by $ln(3)$.
$1-x=-3$
Subtract 1 from both sides.
$-x=-4$
Divide both sides by -1.
$x=4$
