Expert Answers

An illustration of the letter 'A' in a speech bubbles

Solve ln(ln(x))=0:

Use the fact that ln(x) and e^x are inverse functions: in particular, e^(ln(u))=u.

ln(ln(x))=0  Raise both sides with base e:

e^(ln(ln(x)))=e^0  a^0=1 for all a not zero, so:

ln(x)=1  Raise both sides with base e:

e^(ln(x))=e^1

x=e

---------------------------------------------------------------------------------

The solution is e where e is approximately 2.7182818284590; e is the base of the natural logarithm.

---------------------------------------------------------------------------------

Check: ln(ln(e))=ln(1)=0.

The graph of ln(ln(x)):

'

Note that the zero is at approximately 2.7 as expected.

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial