Finite Math Examples

\log_{6} (\frac{36}{x})

$\log_{6} (\frac{36}{x})$

Step 1

Set the denominator in

\frac{36}{x}

$\frac{36}{x}$ equal to

0

$0$ to find where the expression is undefined.

x = 0

$x = 0$

Step 2

Set the argument in

\log_{6} (\frac{36}{x})

$\log_{6} (\frac{36}{x})$ less than or equal to

0

$0$ to find where the expression is undefined.

\frac{36}{x} \leq 0

$\frac{36}{x} \leq 0$

Step 3

Solve for

x

$x$ .

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Step 3.1

Find all the values where the expression switches from negative to positive by setting each factor equal to

0

$0$ and solving.

x = 0

$x = 0$

Step 3.2

Find the domain of

\frac{36}{x}

$\frac{36}{x}$ .

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Step 3.2.1

Set the denominator in

\frac{36}{x}

$\frac{36}{x}$ equal to

0

$0$ to find where the expression is undefined.

x = 0

$x = 0$

Step 3.2.2

The domain is all values of

x

$x$ that make the expression defined.

(- \infty, 0) \cup (0, \infty)

$(- \infty, 0) \cup (0, \infty)$

(- \infty, 0) \cup (0, \infty)

$(- \infty, 0) \cup (0, \infty)$

Step 3.3

The solution consists of all of the true intervals.

x < 0

$x < 0$

x < 0

$x < 0$

Step 4

The equation is undefined where the denominator equals

0

$0$ , the argument of a square root is less than

0

$0$ , or the argument of a logarithm is less than or equal to

0

$0$ .

x \leq 0

$x \leq 0$

(- \infty, 0]

$(- \infty, 0]$

Step 5