Find the Domain f(x) = log base 4 of 5-x

$f (x) = \log_{4} (5 - x)$

Set the argument in $\log_{4} (5 - x)$ greater than $0$ to find where the expression is defined.

$5 - x > 0$

Solve for $x$ .

Subtract $5$ from both sides of the inequality.

$- x > - 5$

Divide each term in $- x > - 5$ by $- 1$ and simplify.

Divide each term in $- x > - 5$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} < \frac{- 5}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} < \frac{- 5}{- 1}$

Divide $x$ by $1$ .

$x < \frac{- 5}{- 1}$

Simplify the right side.

Divide $- 5$ by $- 1$ .

$x < 5$

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

Interval Notation:

$(- \infty, 5)$

Set-Builder Notation:

${x | x < 5}$

Find the Domain f(x) = log base 4 of 5-x

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