Answer:
x = log(1+√2) ≈ 0.38277569
Step-by-step explanation:
Let z = 10^x. Then the equation can be rewritten ...
z^2 -2z -1 = 0
z^2 -2z +1 -2 = 0 . . . . rewrite to a form with a square
(z -1)^2 = 2 . . . . . . . . . add 2
z -1 = ±√2 . . . . . . . . . . square root
z = 1 ± √2 . . . . . . . . . . add 1
From the definition of z, we know it must be positive, so the only viable solution here is ...
z = 10^x = 1+√2
x = log(1+√2)
x ≈ 0.38277569
