Precalculus Examples

$\log (4) (\frac{\sqrt{x^{2} - 9 x}}{3 x - 1})$

Step 1

Rewrite $\log (4)$ as $\log (2^{2})$ .

$\log (2^{2}) \frac{\sqrt{x^{2} - 9 x}}{3 x - 1}$

Step 2

Expand $\log (2^{2})$ by moving $2$ outside the logarithm.

$2 \log (2) \frac{\sqrt{x^{2} - 9 x}}{3 x - 1}$

Step 3

Factor $x$ out of $x^{2} - 9 x$ .

Tap for more steps...

Step 3.1

Factor $x$ out of $x^{2}$ .

$2 \log (2) \frac{\sqrt{x \cdot x - 9 x}}{3 x - 1}$

Step 3.2

Factor $x$ out of $- 9 x$ .

$2 \log (2) \frac{\sqrt{x \cdot x + x \cdot - 9}}{3 x - 1}$

Step 3.3

Factor $x$ out of $x \cdot x + x \cdot - 9$ .

$2 \log (2) \frac{\sqrt{x (x - 9)}}{3 x - 1}$

Step 4

Multiply $2 \log (2) \frac{\sqrt{x (x - 9)}}{3 x - 1}$ .

Tap for more steps...

Step 4.1

Combine $\frac{\sqrt{x (x - 9)}}{3 x - 1}$ and $2$ .

$\frac{\sqrt{x (x - 9)} \cdot 2}{3 x - 1} \log (2)$

Step 4.2

Combine $\frac{\sqrt{x (x - 9)} \cdot 2}{3 x - 1}$ and $\log (2)$ .

$\frac{\sqrt{x (x - 9)} \cdot 2 \log (2)}{3 x - 1}$

Step 5

Move $2$ to the left of $\sqrt{x (x - 9)}$ .

$\frac{2 \sqrt{x (x - 9)} \log (2)}{3 x - 1}$