studying for test but having a hard time with this one not r

studying for test but having a hard time with this one. not really sure abput the proper steps.
any help would be appreciated.

Solution

e^-x+e^x-2=0

multiplying whole equation by e^x

1 +e^2x-2e^x=0

e^2x-2e^x+1=0

(e^x-1)²=0

e^x=1

x = ln 1=0