Question 1197491
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If ln{ln[ln(lnx)]}=0, where the base of each natural log is e, then x=e^k. Find the positive real value of k.
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<pre>
If  ln{ln[ln(lnx)]} = 0,  then

       ln[ln(lnx)]  = 1,  then

          ln(ln(x)) = e, then

             ln(x)  = {{{e^(e)}}},  then

                x   = {{{e^(e^e)}}}.


The problem asks to find such real value "k" that

                x = {{{e^k}}} = {{{e^(e^e)}}}.


So, this value of "k" is  k = {{{e^e}}} = {{{2.71828^2.71828}}} = 15.15421   (approximately).


<U>ANSWER</U>.   k = {{{e^e}}} = {{{2.71828^2.71828}}} = 15.15421   (approximately).
</pre>
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Solved.


Joking math problem with a huge underwater stone.