Solve for x natural log of x>=3

$\ln (x) \geq 3$

Convert the inequality to an equality.

$\ln (x) = 3$

Solve the equation.

To solve for $x$ , rewrite the equation using properties of logarithms.

$e^{\ln (x)} = e^{3}$

Rewrite $\ln (x) = 3$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$e^{3} = x$

Rewrite the equation as $x = e^{3}$ .

$x = e^{3}$

Find the domain of $\ln (x) - 3$ .

Set the argument in $\ln (x)$ greater than $0$ to find where the expression is defined.

$x > 0$

The domain is all values of $x$ that make the expression defined.

$(0, \infty)$

The solution consists of all of the true intervals.

$x \geq e^{3}$

The result can be shown in multiple forms.

Inequality Form:

$x \geq e^{3}$

Interval Notation:

$[e^{3}, \infty)$

Solve for x natural log of x>=3

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