Algebra Examples

$\ln (x) \geq 3$

Step 1

Convert the inequality to an equality.

$\ln (x) = 3$

Step 2

Solve the equation.

Tap for more steps...

Step 2.1

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

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

Step 2.2

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 $b^{y} = x$ .

$e^{3} = x$

Step 2.3

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

$x = e^{3}$

Step 3

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

Tap for more steps...

Step 3.1

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

$x > 0$

Step 3.2

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

$(0, \infty)$

Step 4

The solution consists of all of the true intervals.

$x \geq e^{3}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \geq e^{3}$

Interval Notation:

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

Step 6