Solve ln ( ln ( ln ((e^x) +4)))=e

How to solve this?

ln ( ln ( ln ((e^x) +4)))=e

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Hint: The exponential function is the inverse of the natural logarithm.

I do it in this way:

e^e = ln ( ln ( e^x +4))
e^e^e = ln (e^x +4)
e^e^e^e = e^x +4
x = 20

Is it correct? Or is there any others more easier way?

frozen7 said:
I do it in this way:

e^e = ln ( ln ( e^x +4))
e^e^e = ln (e^x +4)
e^e^e^e = e^x +4
x = 20

Is it correct? Or is there any others more easier way?

Correct. x = ln(e^e^e^e - 4) = 20.08553691561896