Precalculus Examples

$\frac{\log (u)}{3} + \frac{\log (v)}{3} + \frac{\log (w)}{3}$

Step 1

Combine the numerators over the common denominator.

$\frac{\log (u) + \log (v) + \log (w)}{3}$

Step 2

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

$\frac{\log (u v) + \log (w)}{3}$

Step 3

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

$\frac{\log (u v w)}{3}$

Step 4

Rewrite $\frac{\log (u v w)}{3}$ as $\frac{1}{3} \log (u v w)$ .

$\frac{1}{3} \log (u v w)$

Step 5

Simplify $\frac{1}{3} \log (u v w)$ by moving $\frac{1}{3}$ inside the logarithm.

$\log ({(u v w)}^{\frac{1}{3}})$

Step 6

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

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Step 6.1

Apply the product rule to $u v w$ .

$\log ({(u v)}^{\frac{1}{3}} w^{\frac{1}{3}})$

Step 6.2

Apply the product rule to $u v$ .

$\log (u^{\frac{1}{3}} v^{\frac{1}{3}} w^{\frac{1}{3}})$