An equation involving logarithms

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Question from mindy, a parent:

Hi,
I am trying to find x, the equation is:
log_2(log x + 2 (log x)^(1/2) + 1) - 2 log_4((log x)^(1/2) + 1) = 1

Thank you very much for your time. =)

Hi Mindy,

I can help get you started. First of all

If t = log₄(s) then 4^t = s which can be written (2²)^t = 2^2t = s and hence 2t = log₂(s).
Substituting t = log₄(s) you get 2 log₄(s) = log₂(s).

Thus you equation can be rewritten

log₂[log x + 2 (log x)^1/2 + 1] - log₂[(log x)^1/2 + 1] = 1

Now you can use two properties of logarithm functions.

Can you complete the problem now?

Write back if you need more assistance,
Harley

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