Precalculus Examples

$\frac{1}{2} (\log (a) + \log (b))$

Step 1

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

$\frac{1}{2} \cdot \log (a b)$

Step 2

Simplify $\frac{1}{2} \log (a b)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log ({(a b)}^{\frac{1}{2}})$

Step 3

Apply the product rule to $a b$ .

$\log (a^{\frac{1}{2}} b^{\frac{1}{2}})$