Precalculus Examples

$\log_{4} (x (x - 9))$

Step 1

Apply the distributive property.

$\log_{4} (x \cdot x + x \cdot - 9)$

Step 2

Simplify the expression.

Tap for more steps...

Step 2.1

Multiply $x$ by $x$ .

$\log_{4} (x^{2} + x \cdot - 9)$

Step 2.2

Move $- 9$ to the left of $x$ .

$\log_{4} (x^{2} - 9 x)$

Step 3

Rewrite $\log_{4} (x^{2} - 9 x)$ using the change of base formula.

Tap for more steps...

Step 3.1

The change of base rule can be used if $a$ and $b$ are greater than $0$ and not equal to $1$ , and $x$ is greater than $0$ .

$\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}$

Step 3.2

Substitute in values for the variables in the change of base formula, using $b = 10$ .

$\frac{\log (x^{2} - 9 x)}{\log (4)}$