Precalculus Examples

$\log_{8} (y) + \log_{8} (z) + \log_{8} (w) + \frac{\log_{8} (x)}{3}$

Step 1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log_{8} (y z) + \log_{8} (w) + \frac{\log_{8} (x)}{3}$

Step 2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log_{8} (y z w) + \frac{\log_{8} (x)}{3}$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Rewrite $\frac{\log_{8} (x)}{3}$ as $\frac{1}{3} \log_{8} (x)$ .

$\log_{8} (y z w) + \frac{1}{3} \log_{8} (x)$

Step 3.2

Simplify $\frac{1}{3} \log_{8} (x)$ by moving $\frac{1}{3}$ inside the logarithm.

$\log_{8} (y z w) + \log_{8} (x^{\frac{1}{3}})$

Step 4

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log_{8} (y z w x^{\frac{1}{3}})$