Tangent line on $ e^x $ which is parallel to $y=2x$
The definition of two lines being parallel is that they have the same slope.
For any point on $y_1=e^x$, the slope is $y_1'=e^x$
For any point on $y_2=2x$, the slope is $y_2' = 2$
We want to find the parallel line, so let $y_1'=y_2'$
$\implies e^x=2$
Take the natural log,
$\implies x=ln2$
We want to find the point on $y_1$, so we subsitute $x$ in,
$\implies (x,y)=(x,e^x)=(ln2,2)$