Solve the Inequality for x e^x>4

$e^{x} > 4$

Step 1

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (e^{x}) > \ln (4)$

Step 2

Expand the left side.

Expand $\ln (e^{x})$ by moving $x$ outside the logarithm.

$x \ln (e) > \ln (4)$

The natural logarithm of $e$ is $1$ .

$x \cdot 1 > \ln (4)$

Multiply $x$ by $1$ .

$x > \ln (4)$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x > \ln (4)$

Interval Notation:

$(\ln (4), \infty)$

Step 4