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e^(e^x) = 2

Date: 01/28/2002 at 00:40:52
From: elizabeth grayson
Subject: e

I have been fruitlessly trying to solve e^(e^x) = 2. Help!

Date: 01/28/2002 at 12:22:35
From: Doctor Paul
Subject: Re: e

Take the ln of both sides to obtain:

e^x * ln(e) = ln(2)

but ln(e) = 1

so we have e^x = ln(2)

repeat the process to obtain:

x = ln(ln(2))

I hope this helps.  Please write back if you'd like to talk about this 
some more.

- Doctor Paul, The Math Forum   
Associated Topics:
High School Calculus

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