Precalculus Examples

$\frac{1}{2} \cdot \log_{2} (x) + \log_{2} (y)$

Step 1

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

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

Step 2

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

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

Step 3

Reorder factors in $\log_{2} (x^{\frac{1}{2}} y)$ .

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