Answer
The calculated value for $x$ are ln$3$ and ln$(-2)$.
Work Step by Step
Given: $e^{2x}-e^{x}-6=0$
Suppose $e^{x} = t$
Then
$t^{2}-t-6=0$ gives $t=3,-2$
Thus, $e^{x} = 3,-2$
For $e^{x} = 3$
$x=$ln $3$
For $e^{x} = -2$
$lne^{x}=ln(-2)$
This implies $x=ln(-2)$
Hence, the calculated value for $x$ are ln3 and ln(-2).