How do you solve for x in the equation ln(ln(x)) = 1?

To solve the equation ln(ln(x)) = 1, we start by isolating the natural logarithm term.

First, we exponentiate both sides of the equation to eliminate the outer logarithm:

ln(x) = e1

This simplifies to:

ln(x) = e

Next, we exponentiate again to solve for x:

x = ee

Finally, we find that the solution to the original equation is:

x = ee

Thus, the solution to the equation ln(ln(x)) = 1 is x = e^e.