Find the Domain f(x) = log of 4x-1

$f (x) = \log (4 x - 1)$

Set the argument in $\log (4 x - 1)$ greater than $0$ to find where the expression is defined.

$4 x - 1 > 0$

Solve for $x$ .

Add $1$ to both sides of the inequality.

$4 x > 1$

Divide each term in $4 x > 1$ by $4$ and simplify.

Divide each term in $4 x > 1$ by $4$ .

$\frac{4 x}{4} > \frac{1}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} > \frac{1}{4}$

Divide $x$ by $1$ .

$x > \frac{1}{4}$

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(\frac{1}{4}, \infty)$

Set-Builder Notation:

${x | x > \frac{1}{4}}$