Calculus Examples

$e^{x} > 5$

Step 1

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

$\ln (e^{x}) > \ln (5)$

Step 2

Expand the left side.

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Step 2.1

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

$x \ln (e) > \ln (5)$

Step 2.2

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

$x \cdot 1 > \ln (5)$

Step 2.3

Multiply $x$ by $1$ .

$x > \ln (5)$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x > \ln (5)$

Interval Notation:

$(\ln (5), \infty)$

Step 4