Calculus Examples

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

Step 1

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

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

Step 2

Rewrite $\log_{8} (4 a)$ using the change of base formula.

Tap for more steps...

Step 2.1

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 $0$ .

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

Step 2.2

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

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

Step 3

Factor $\frac{\log (4 a)}{\log (8)}$ out of $\frac{\frac{\log (4 a)}{\log (8)} (b - 4)}{c^{4}}$ .

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

Step 4

Multiply $\frac{\log (4 a)}{\log (8)}$ by $\frac{b - 4}{c^{4}}$ .

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

Step 5

Reorder factors in $\frac{\log (4 a) (b - 4)}{\log (8) c^{4}}$ .

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