Algebra Examples

$\log_{8} (4 a) (\frac{b - 4}{c^{4}})$

Step 1

Rewrite $\log_{8} (4 a)$ as $\log_{8} (4) + \log_{8} (a)$ .

$(\log_{8} (4) + \log_{8} (a)) \frac{b - 4}{c^{4}}$

Step 2

Logarithm base $8$ of $4$ is $\frac{2}{3}$ .

$(\frac{2}{3} + \log_{8} (a)) \frac{b - 4}{c^{4}}$

Step 3

Multiply $\frac{2}{3} + \log_{8} (a)$ by $\frac{b - 4}{c^{4}}$ .

$\frac{(\frac{2}{3} + \log_{8} (a)) (b - 4)}{c^{4}}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

To write $\log_{8} (a)$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{(\frac{2}{3} + \log_{8} (a) \cdot \frac{3}{3}) (b - 4)}{c^{4}}$

Step 4.2

Combine $\log_{8} (a)$ and $\frac{3}{3}$ .

$\frac{(\frac{2}{3} + \frac{\log_{8} (a) \cdot 3}{3}) (b - 4)}{c^{4}}$

Step 4.3

Combine the numerators over the common denominator.

$\frac{\frac{2 + \log_{8} (a) \cdot 3}{3} (b - 4)}{c^{4}}$

Step 4.4

Move $3$ to the left of $\log_{8} (a)$ .

$\frac{\frac{2 + 3 \log_{8} (a)}{3} (b - 4)}{c^{4}}$

Step 5

Factor $\frac{2 + 3 \log_{8} (a)}{3}$ out of $\frac{\frac{2 + 3 \log_{8} (a)}{3} (b - 4)}{c^{4}}$ .

$\frac{2 + 3 \log_{8} (a)}{3} \cdot \frac{b - 4}{c^{4}}$

Step 6

Multiply $\frac{2 + 3 \log_{8} (a)}{3}$ by $\frac{b - 4}{c^{4}}$ .

$\frac{(2 + 3 \log_{8} (a)) (b - 4)}{3 c^{4}}$