domain of ln(ln(x^2+2))

Let's find the domain of

\ln (\ln (x^{2} + 2))

For the expression

\ln (\ln (x^{2} + 2))

to be defined, the following condition is necessary:

\ln (x^{2} + 2) > 0

For the expression

\ln (x^{2} + 2)

to be defined, the following condition is necessary:

x^{2} + 2 > 0

The condition

\ln (x^{2} + 2) > 0

is always true on its real domain

The condition

x^{2} + 2 > 0

is always true on its real domain

ⓘ This expression imposes no restriction on the real variable

▶Domain of definition:

x \in ℝ

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