Precalculus Examples

$f (x) = \log_{2} (5 x - 4)$

Step 1

Set the argument of the logarithm equal to zero.

$5 x - 4 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $4$ to both sides of the equation.

$5 x = 4$

Step 2.2

Divide each term in $5 x = 4$ by $5$ and simplify.

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Step 2.2.1

Divide each term in $5 x = 4$ by $5$ .

$\frac{5 x}{5} = \frac{4}{5}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $5$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{4}{5}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{4}{5}$

Step 3

The vertical asymptote occurs at $x = \frac{4}{5}$ .

Vertical Asymptote: $x = \frac{4}{5}$

Step 4