Answer
$x=\dfrac{6}{5}$
Work Step by Step
$e^{1-2x}=e^{3x-5}$
Simply use the one-to-one property to solve this equation. Make the exponents on both sides of the equation equal:
$1-2x=3x-5$
Take the $3x$ to the left side of the equation and take the $1$ to the right side:
$-2x-3x=-5-1$
Simplify both sides:
$-5x=-6$
Solve for $x$:
$x=\dfrac{6}{5}$