why lim x->1 (ln|lnx|) =-∞ not +∞???

[thanh loan]

when i learn math about lim, i don't understand that WHY lim x->1 (ln|lnx|) =-∞, not +∞? who can help me ?
Many thanks! :* :X

 

[Deleted member 4993]

when i learn math about lim, i don't understand that WHY lim x->1 (ln|lnx|) =-∞, not +∞? who can help me ?
Many thanks! :* :X

Using a graphing calculator or wolframalpha.com - plot y = ln(|ln(x)|)

Then look at the behavior of the function in the vicinity of x = 1.

 

[pka]

when i learn math about lim, i don't understand that WHY lim x->1 (ln|lnx|) =-∞, not +∞? who can help me ?

We use the continuity of \(\displaystyle \left| x \right|\).

Recall that \(\displaystyle {\lim _{x \to 1}}\ln (x) = - \infty \) so
\(\displaystyle {\lim _{x \to 1}}\ln \left( {\left| {\ln (x)} \right|} \right) = \ln \left| {\left( {{{\lim }_{x \to 1}}\ln (x)} \right)} \right|=~?\)