Find the Domain y = log of 2+4x

$y = \log (2 + 4 x)$

Step 1

Set the argument in $\log (2 + 4 x)$ greater than $0$ to find where the expression is defined.

$2 + 4 x > 0$

Step 2

Solve for $x$ .

Subtract $2$ from both sides of the inequality.

$4 x > - 2$

Divide each term in $4 x > - 2$ by $4$ and simplify.

Divide each term in $4 x > - 2$ by $4$ .

$\frac{4 x}{4} > \frac{- 2}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} > \frac{- 2}{4}$

Divide $x$ by $1$ .

$x > \frac{- 2}{4}$

Simplify the right side.

Cancel the common factor of $- 2$ and $4$ .

Factor $2$ out of $- 2$ .

$x > \frac{2 (- 1)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 3

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

Interval Notation:

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

Set-Builder Notation:

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

Step 4