Answer
$x=1$
Work Step by Step
$3^{2x}-3^{x}-6=0$
Let $3^{x}$ be equal to $u$:
$u=3^{x}$
$u^{2}=3^{2x}$
Rewrite the original equation using the new variable $u$:
$u^{2}-u-6=0$
Solve this equation by factoring:
$(u-3)(u+2)=0$
Set both factors equal to $0$ and solve each individual equation for $u$:
$u-3=0$
$u=3$
$u+2=0$
$u=-2$
Substitute $u$ back to $3^{x}$ and solve for $x$:
$3^{x}=3$
If $3^{x}=3$, then $x=1$
$x=1$
$3^{x}=-2$
There are no values of $x$ that make this equation true.
The solution found is $x=1$
