Precalculus Examples

$\frac{\log_{7} (x)}{2} + \frac{\log_{7} (y)}{2} + \frac{\log_{7} (z)}{2}$

Step 1

Combine the numerators over the common denominator.

$\frac{\log_{7} (x) + \log_{7} (y) + \log_{7} (z)}{2}$

Step 2

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

$\frac{\log_{7} (x y) + \log_{7} (z)}{2}$

Step 3

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

$\frac{\log_{7} (x y z)}{2}$

Step 4

Rewrite $\frac{\log_{7} (x y z)}{2}$ as $\frac{1}{2} \log_{7} (x y z)$ .

$\frac{1}{2} \log_{7} (x y z)$

Step 5

Simplify $\frac{1}{2} \log_{7} (x y z)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log_{7} ({(x y z)}^{\frac{1}{2}})$

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 $x y z$ .

$\log_{7} ({(x y)}^{\frac{1}{2}} z^{\frac{1}{2}})$

Step 6.2

Apply the product rule to $x y$ .

$\log_{7} (x^{\frac{1}{2}} y^{\frac{1}{2}} z^{\frac{1}{2}})$