ln(x^2)=2 — step-by-step solution

Let's solve in

ℝ

\ln (x^{2}) = 2

On the logarithm's domain, ln is strictly increasing:

\ln (x^{2}) = 2

is equivalent to

x^{2} = e^{2}

The two numbers whose square is

e^{2}

are

- e

and

e

Candidates, pending the domain check:

x = {- e, e}

Let's find the domain of

\ln (x^{2}) = 2

For the expression

\ln (x^{2})

to exist, you must check:

x^{2} > 0

Any even power is always non-negative in ℝ and equals 0 only when the base itself is 0

Domain constraints:

x \neq 0

▶Solution:

x = {- e, e}

The numeric value of:

x = {- e, e}

equals:

▷

x = {\approx -2.7183, \approx 2.7183}