Linear Algebra Examples

$\log (\frac{40000}{x}) = (\frac{12}{20}) \log (2)$

Step 1

Set the argument in $\log (\frac{40000}{x})$ greater than $0$ to find where the expression is defined.

$\frac{40000}{x} > 0$

Step 2

Solve for $x$ .

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Step 2.1

Find all the values where the expression switches from negative to positive by setting each factor equal to $0$ and solving.

$x = 0$

Step 2.2

Find the domain of $\frac{40000}{x}$ .

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Step 2.2.1

Set the denominator in $\frac{40000}{x}$ equal to $0$ to find where the expression is undefined.

$x = 0$

Step 2.2.2

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

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

Step 2.3

The solution consists of all of the true intervals.

$x > 0$

Step 3

Set the denominator in $\frac{40000}{x}$ equal to $0$ to find where the expression is undefined.

$x = 0$

Step 4

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

Interval Notation:

$(0, \infty)$

Set-Builder Notation:

${x | x > 0}$

Step 5