Finite Math Examples

$\log_{3} (7 - x)$

Step 1

Set the argument in $\log_{3} (7 - x)$ less than or equal to $0$ to find where the expression is undefined.

$7 - x \leq 0$

Step 2

Solve for $x$ .

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Step 2.1

Subtract $7$ from both sides of the inequality.

$- x \leq - 7$

Step 2.2

Divide each term in $- x \leq - 7$ by $- 1$ and simplify.

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Step 2.2.1

Divide each term in $- x \leq - 7$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \geq \frac{- 7}{- 1}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} \geq \frac{- 7}{- 1}$

Step 2.2.2.2

Divide $x$ by $1$ .

$x \geq \frac{- 7}{- 1}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $- 7$ by $- 1$ .

$x \geq 7$

Step 3

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$x \geq 7$

$[7, \infty)$

Step 4