Find the Domain y = log of 5+6x

$y = \log (5 + 6 x)$

Set the argument in $\log (5 + 6 x)$ greater than $0$ to find where the expression is defined.

$5 + 6 x > 0$

Solve for $x$ .

Subtract $5$ from both sides of the inequality.

$6 x > - 5$

Divide each term in $6 x > - 5$ by $6$ and simplify.

Divide each term in $6 x > - 5$ by $6$ .

$\frac{6 x}{6} > \frac{- 5}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} > \frac{- 5}{6}$

Divide $x$ by $1$ .

$x > \frac{- 5}{6}$

Simplify the right side.

Move the negative in front of the fraction.

$x > - \frac{5}{6}$

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

Interval Notation:

$(- \frac{5}{6}, \infty)$

Set-Builder Notation:

${x | x > - \frac{5}{6}}$