Precalculus Examples

$\ln (x) + 2 = 5$

Step 1

Move all terms not containing $\ln (x)$ to the right side of the equation.

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Step 1.1

Subtract $2$ from both sides of the equation.

$\ln (x) = 5 - 2$

Step 1.2

Subtract $2$ from $5$ .

$\ln (x) = 3$

Step 2

To solve for $x$ , rewrite the equation using properties of logarithms.

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

Step 3

Rewrite $\ln (x) = 3$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$e^{3} = x$

Step 4

Rewrite the equation as $x = e^{3}$ .

$x = e^{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = e^{3}$

Decimal Form:

$x = 20.08553692 \dots$

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