Calculus Examples

$\ln (1 - x y)$

Step 1

Set the argument in $\ln (1 - x y)$ greater than $0$ to find where the expression is defined.

$1 - x y > 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Subtract $1$ from both sides of the inequality.

$- x y > - 1$

Step 2.2

Divide each term in $- x y > - 1$ by $- y$ and simplify.

Tap for more steps...

Step 2.2.1

Divide each term in $- x y > - 1$ by $- y$ .

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

Step 2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.1

Dividing two negative values results in a positive value.

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

Step 2.2.2.2

Cancel the common factor of $y$ .

Tap for more steps...

Step 2.2.2.2.1

Cancel the common factor.

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

Step 2.2.2.2.2

Divide $x$ by $1$ .

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

Step 2.2.3

Simplify the right side.

Tap for more steps...

Step 2.2.3.1

Dividing two negative values results in a positive value.

$x > \frac{1}{y}$

Step 2.3

Use each root to create test intervals.

$x < \frac{1}{y}$

$x > \frac{1}{y}$

Step 2.4

Compare the intervals to determine which ones satisfy the original inequality.

Step 2.5

Since there are no numbers that fall within the interval, this inequality has no solution.

No solution

Step 3

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4