Linear Algebra Examples

$\frac{e^{3 x}}{3 \cdot e^{4 x}}$

Step 1

Set the denominator in $\frac{e^{3 x}}{3 \cdot e^{4 x}}$ equal to $0$ to find where the expression is undefined.

$3 \cdot e^{4 x} = 0$

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.

$\ln (3 \cdot e^{4 x}) = \ln (0)$

Step 2.2

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

Undefined

Step 2.3

There is no solution for $3 \cdot e^{4 x} = 0$

No solution

Step 3

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4