Precalculus Examples

$\log ({(a b c d)}^{\frac{1}{7}})$

Step 1

Expand $\log ({(a b c d)}^{\frac{1}{7}})$ by moving $\frac{1}{7}$ outside the logarithm.

$\frac{1}{7} \log (a b c d)$

Step 2

Rewrite $\log (a b c d)$ as $\log (a b c) + \log (d)$ .

$\frac{1}{7} (\log (a b c) + \log (d))$

Step 3

Rewrite $\log (a b c)$ as $\log (a b) + \log (c)$ .

$\frac{1}{7} (\log (a b) + \log (c) + \log (d))$

Step 4

Rewrite $\log (a b)$ as $\log (a) + \log (b)$ .

$\frac{1}{7} (\log (a) + \log (b) + \log (c) + \log (d))$

Step 5

Apply the distributive property.

$\frac{1}{7} \log (a) + \frac{1}{7} \log (b) + \frac{1}{7} \log (c) + \frac{1}{7} \log (d)$

Step 6

Simplify.

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Step 6.1

Combine $\frac{1}{7}$ and $\log (a)$ .

$\frac{\log (a)}{7} + \frac{1}{7} \log (b) + \frac{1}{7} \log (c) + \frac{1}{7} \log (d)$

Step 6.2

Combine $\frac{1}{7}$ and $\log (b)$ .

$\frac{\log (a)}{7} + \frac{\log (b)}{7} + \frac{1}{7} \log (c) + \frac{1}{7} \log (d)$

Step 6.3

Combine $\frac{1}{7}$ and $\log (c)$ .

$\frac{\log (a)}{7} + \frac{\log (b)}{7} + \frac{\log (c)}{7} + \frac{1}{7} \log (d)$

Step 6.4

Combine $\frac{1}{7}$ and $\log (d)$ .

$\frac{\log (a)}{7} + \frac{\log (b)}{7} + \frac{\log (c)}{7} + \frac{\log (d)}{7}$