Find the Domain y = log of -9x

$y = \log (- 9 x)$

Step 1

Set the argument in $\log (- 9 x)$ greater than $0$ to find where the expression is defined.

$- 9 x > 0$

Step 2

Divide each term in $- 9 x > 0$ by $- 9$ and simplify.

Divide each term in $- 9 x > 0$ by $- 9$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 9 x}{- 9} < \frac{0}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 x}{- 9} < \frac{0}{- 9}$

Divide $x$ by $1$ .

$x < \frac{0}{- 9}$

Simplify the right side.

Divide $0$ by $- 9$ .

$x < 0$

Step 3

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

Interval Notation:

$(- \infty, 0)$

Set-Builder Notation:

${x | x < 0}$

Step 4

Find the Domain y = log of -9x

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