Question

ln(e) = ln(√(2)/x) -ln(e)

Answer 1

2 ln e = ln e^2
so
ln e^2 = ln (sqrt 2 / x)

e^2 = sqrt 2/x

x = sqrt 2 / e^2

Answer 2

ln e = 1 , so your equation becomes

1 = ln(√(2/x) - 1
2 = ln √(2/x)
√(2/x) = e^2
square both sides
2/x = e^4
x = 2/e^4

notice how I read your expression
If you meant
ln e = ln (√2 /x) - ln 2
2 = ln (√2/x)
√2/x = e^2
x = √2/e^2