Linear Algebra Examples

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

Step 1

Set the argument in $\ln (e^{5 x})$ greater than $0$ to find where the expression is defined.

$e^{5 x} > 0$

Step 2

Solve for $x$ .

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Step 2.1

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

$\ln (e^{5 x}) > \ln (0)$

Step 2.2

The equation cannot be solved because $\ln (0)$ is undefined.

Undefined

Step 2.3

There is no solution for $e^{5 x} > 0$

No solution

Step 3

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4