How to calculate that the x power of e divided by the - x power of e equals 1 / 2,

How to calculate that the x power of e divided by the - x power of e equals 1 / 2,

(e^x)/(e^(-x))
=e^(2x)=1/2
Then 2x = ln (1 / 2) = - LN2
Then x = - LN2 / 2
Where ^ is the power, LN is the log based on E,