Finite Math Examples

$g (x) = 2 - \ln (x + 4)$

Step 1

Set $2 - \ln (x + 4)$ equal to $0$ .

$2 - \ln (x + 4) = 0$

Step 2

Solve for $x$ .

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Step 2.1

Subtract $2$ from both sides of the equation.

$- \ln (x + 4) = - 2$

Step 2.2

Divide each term in $- \ln (x + 4) = - 2$ by $- 1$ and simplify.

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Step 2.2.1

Divide each term in $- \ln (x + 4) = - 2$ by $- 1$ .

$\frac{- \ln (x + 4)}{- 1} = \frac{- 2}{- 1}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Dividing two negative values results in a positive value.

$\frac{\ln (x + 4)}{1} = \frac{- 2}{- 1}$

Step 2.2.2.2

Divide $\ln (x + 4)$ by $1$ .

$\ln (x + 4) = \frac{- 2}{- 1}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $- 2$ by $- 1$ .

$\ln (x + 4) = 2$

Step 2.3

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

$e^{\ln (x + 4)} = e^{2}$

Step 2.4

Rewrite $\ln (x + 4) = 2$ 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 $b^{y} = x$ .

$e^{2} = x + 4$

Step 2.5

Solve for $x$ .

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Step 2.5.1

Rewrite the equation as $x + 4 = e^{2}$ .

$x + 4 = e^{2}$

Step 2.5.2

Subtract $4$ from both sides of the equation.

$x = e^{2} - 4$

Step 3