Solve x if ln(ln(x)) = 4

Sunday, September 13, 2015

The logarithmic equation $\displaystyle{\ln{{\left({\ln{{\left({x}\right)}}}\right)}}}={4}$ has to be solved
for x.

ln is used to denote natural logarithm which is
logarithm to the base e.

$\displaystyle{\ln{{\left({\ln{{\left({x}\right)}}}\right)}}}={4}$ can be rewritten
as:

$\displaystyle{\log}_{{e}}{\left({\log}_{{e}}{x}\right)}={4}$

If
$\displaystyle{\log}_{{b}}{a}={c}$ , we can write $\displaystyle{a}={{b}}^{{c}}$

This gives: $\displaystyle{\log}_{{e}}{x}$
= e^4

Again doing the
same.

$\displaystyle{x}={{e}}^{{{{e}}^{{4}}}}$

The root
of the equation $\displaystyle{\ln{{\left({\ln{{\left({x}\right)}}}\right)}}}={4}$ is $\displaystyle{x}={{e}}^{{{{e}}^{{4}}}}$

Notes