Find the Domain y = log base 5 of 2x-1

$y = \log_{5} (2 x - 1)$

Set the argument in $\log_{5} (2 x - 1)$ greater than $0$ to find where the expression is defined.

$2 x - 1 > 0$

Solve for $x$ .

Add $1$ to both sides of the inequality.

$2 x > 1$

Divide each term in $2 x > 1$ by $2$ and simplify.

Divide each term in $2 x > 1$ by $2$ .

$\frac{2 x}{2} > \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} > \frac{1}{2}$

Divide $x$ by $1$ .

$x > \frac{1}{2}$

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

Interval Notation:

$(\frac{1}{2}, \infty)$

Set-Builder Notation:

${x | x > \frac{1}{2}}$