Precalculus Examples

$\frac{\log_{9} (x)}{3} + \frac{\log_{9} (y)}{3} + \frac{\log_{9} (z)}{3}$

Combine the numerators over the common denominator.

$\frac{\log_{9} (x) + \log_{9} (y) + \log_{9} (z)}{3}$

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

$\frac{\log_{9} (x y) + \log_{9} (z)}{3}$

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

$\frac{\log_{9} (x y z)}{3}$

Rewrite $\frac{\log_{9} (x y z)}{3}$ as $\frac{1}{3} \log_{9} (x y z)$ .

$\frac{1}{3} \log_{9} (x y z)$

Simplify $\frac{1}{3} \log_{9} (x y z)$ by moving $\frac{1}{3}$ inside the logarithm.

$\log_{9} ({(x y z)}^{\frac{1}{3}})$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Tap for more steps...

Apply the product rule to $x y z$ .

$\log_{9} ({(x y)}^{\frac{1}{3}} z^{\frac{1}{3}})$

Apply the product rule to $x y$ .

$\log_{9} (x^{\frac{1}{3}} y^{\frac{1}{3}} z^{\frac{1}{3}})$