Precalculus Examples

$\ln (4 + x) = 3$

Step 1

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

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

Step 2

Rewrite $\ln (4 + x) = 3$ 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 $b^{y} = x$ .

$e^{3} = 4 + x$

Step 3

Solve for $x$ .

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Step 3.1

Rewrite the equation as $4 + x = e^{3}$ .

$4 + x = e^{3}$

Step 3.2

Subtract $4$ from both sides of the equation.

$x = e^{3} - 4$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = e^{3} - 4$

Decimal Form:

$x = 16.08553692 \dots$