Limit of the function log(log(x))

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 lim  log(log(x))
x->-oo

\lim_{x \to -\infty} \log{\left(\log{\left(x \right)} \right)}

Limit(log(log(x)), x, -oo)

Lopital's rule

There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type

The graph

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Rapid solution [src]

oo

\infty

Expand and simplify

Other limits x→0, -oo, +oo, 1

\lim_{x \to -\infty} \log{\left(\log{\left(x \right)} \right)} = \infty

\lim_{x \to \infty} \log{\left(\log{\left(x \right)} \right)} = \infty

\lim_{x \to 0^-} \log{\left(\log{\left(x \right)} \right)} = \infty

\lim_{x \to 0^+} \log{\left(\log{\left(x \right)} \right)} = \infty

\lim_{x \to 1^-} \log{\left(\log{\left(x \right)} \right)} = -\infty

\lim_{x \to 1^+} \log{\left(\log{\left(x \right)} \right)} = -\infty

The graph