That would be great if you could show the steps. Thanks! :D

Note that since e^(x) = 1/e^x, we have:
e^x  1/e^x = 1.
Now, let u = e^x. Applying this substitution gives:
u  1/u = 1.
Multiplying both sides by u yields:
u^2  1 = u ==> u^2  u  1 = 0.
Using the Quadratic Formula:
u = (1 ± √5)/2.
However, note that since u = e^x and e^x > 0 for all x, we require that u > 0. Only the positive value of the plusorminus sign will make u > 0, so:
u = e^x = (1 + √5)/2.
Taking the natural logarithm of both sides yields the final answer to be:
x = ln[(1 + √5)/2].
I hope this helps!
e^x  1/e^x = 1.
Now, let u = e^x. Applying this substitution gives:
u  1/u = 1.
Multiplying both sides by u yields:
u^2  1 = u ==> u^2  u  1 = 0.
Using the Quadratic Formula:
u = (1 ± √5)/2.
However, note that since u = e^x and e^x > 0 for all x, we require that u > 0. Only the positive value of the plusorminus sign will make u > 0, so:
u = e^x = (1 + √5)/2.
Taking the natural logarithm of both sides yields the final answer to be:
x = ln[(1 + √5)/2].
I hope this helps!

Let y = e^x. Note y>0. Then
y  1/y = 1.
y^2  y  1 = 0
The only positive root is y = (sqrt(5)+1)/2. 1/y = (sqrt(5)1)/2.
x = ln(y) = ln( (sqrt(5)+1)/2 ).
y  1/y = 1.
y^2  y  1 = 0
The only positive root is y = (sqrt(5)+1)/2. 1/y = (sqrt(5)1)/2.
x = ln(y) = ln( (sqrt(5)+1)/2 ).

megaone

I think x is 0.