Find the Domain y = log of 3+5x

$y = \log (3 + 5 x)$

Step 1

Set the argument in $\log (3 + 5 x)$ greater than $0$ to find where the expression is defined.

$3 + 5 x > 0$

Step 2

Solve for $x$ .

Subtract $3$ from both sides of the inequality.

$5 x > - 3$

Divide each term in $5 x > - 3$ by $5$ and simplify.

Divide each term in $5 x > - 3$ by $5$ .

$\frac{5 x}{5} > \frac{- 3}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} > \frac{- 3}{5}$

Divide $x$ by $1$ .

$x > \frac{- 3}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x > - \frac{3}{5}$

Step 3

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

Interval Notation:

$(- \frac{3}{5}, \infty)$

Set-Builder Notation:

${x | x > - \frac{3}{5}}$

Step 4