Precalculus Examples

$5 + \ln (x + 2) = 6$

Step 1

Move all terms not containing $\ln (x + 2)$ to the right side of the equation.

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Step 1.1

Subtract $5$ from both sides of the equation.

$\ln (x + 2) = 6 - 5$

Step 1.2

Subtract $5$ from $6$ .

$\ln (x + 2) = 1$

Step 2

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

$e^{\ln (x + 2)} = e^{1}$

Step 3

Rewrite $\ln (x + 2) = 1$ 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 $b^{y} = x$ .

$e^{1} = x + 2$

Step 4

Solve for $x$ .

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Step 4.1

Rewrite the equation as $x + 2 = e^{1}$ .

$x + 2 = e$

Step 4.2

Subtract $2$ from both sides of the equation.

$x = e - 2$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = e - 2$

Decimal Form:

$x = 0.71828182 \dots$