Precalculus Examples

$f (x) = \ln (6 - x)$

Step 1

Set the argument of the logarithm equal to zero.

$6 - x = 0$

Step 2

Solve for $x$ .

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Step 2.1

Subtract $6$ from both sides of the equation.

$- x = - 6$

Step 2.2

Divide each term in $- x = - 6$ by $- 1$ and simplify.

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Step 2.2.1

Divide each term in $- x = - 6$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 6}{- 1}$

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.

$\frac{x}{1} = \frac{- 6}{- 1}$

Step 2.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 6}{- 1}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $- 6$ by $- 1$ .

$x = 6$

Step 3

The vertical asymptote occurs at $x = 6$ .

Vertical Asymptote: $x = 6$

Step 4