domain(ln(sqrt(x)-2)+sqrt(x))

Let's find the domain of

\ln (\sqrt{x} - 2) + \sqrt{x}

For the expression

\ln (\sqrt{x} - 2)

to be defined, the following condition is necessary:

\sqrt{x} - 2 > 0

For the expression

\sqrt{x}

to be defined, the following condition is necessary:

x \geq 0

We solve in

ℝ

\sqrt{x} - 2 > 0

We isolate the square root:

\sqrt{x} > 2

. Since both sides are nonnegative, square both sides, which keeps the direction of the inequality:

x > 2^{2}

ⓘ A power with a positive integer exponent is a repeated product:

2^{2}

2 \cdot 2

4

Solution found:

x > 4

Intersecting

x > 4

and

x \geq 0

gives

x > 4

▶Domain of definition:

x > 4

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