Precalculus Examples

$\ln (x - 5) > e^{0.025 x}$

Step 1

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 8.43784886$

Step 2

Find the domain of $\ln (x - 5) - e^{0.025 x}$ .

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Step 2.1

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

$x - 5 > 0$

Step 2.2

Add $5$ to both sides of the inequality.

$x > 5$

Step 2.3

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

$(5, \infty)$

Step 3

The solution consists of all of the true intervals.

$x > 8.43784886$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > 8.43784886$

Interval Notation:

$(8.43784886, \infty)$

Step 5