Precalculus Examples

$\frac{1}{2} \cdot (\log_{4} (a)) + \log_{4} (b)$

Step 1

Simplify $\frac{1}{2} (\log_{4} (a))$ by moving $\frac{1}{2}$ inside the logarithm.

$\log_{4} (a^{\frac{1}{2}}) + \log_{4} (b)$

Step 2

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

$\log_{4} (a^{\frac{1}{2}} b)$

Step 3

Reorder factors in $\log_{4} (a^{\frac{1}{2}} b)$ .

$\log_{4} (b a^{\frac{1}{2}})$