Answer
$x=\dfrac{1}{2}$
Work Step by Step
$3^{4x}-3^{2x}-6=0$
Rewrite the first term of this equation as $(3^{2x})^{2}$:
$(3^{2x})^{2}-3^{2x}-6=0$
Factor this equation:
$(3^{2x}-3)(3^{2x}+2)=0$
Set both factors equal to $0$ and solve each individual equation:
$3^{2x}+2=0$
Take the $2$ to the right side:
$3^{2x}=-2$
Since no values of $x$ make this first equation true, it has no solution. Let's move on to the other one:
$3^{2x}-3=0$
Take the $3$ to the right side:
$3^{2x}=3$
Simply use the one-to-one property to solve this equation.
$3^{2x}=3$
$2x=1$
Solve for $x$:
$x=\dfrac{1}{2}$