Find the Domain y = log of -7x

$y = \log (- 7 x)$

Step 1

Set the argument in $\log (- 7 x)$ greater than $0$ to find where the expression is defined.

$- 7 x > 0$

Step 2

Divide each term in $- 7 x > 0$ by $- 7$ and simplify.

Divide each term in $- 7 x > 0$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 x}{- 7} < \frac{0}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} < \frac{0}{- 7}$

Divide $x$ by $1$ .

$x < \frac{0}{- 7}$

Simplify the right side.

Divide $0$ by $- 7$ .

$x < 0$

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 -7x

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