Simplify/Condense 1/2 log base 8 of x+ log base 8 of y

$\frac{1}{2} \log_{8} (x) + \log_{8} (y)$

Simplify $\frac{1}{2} \log_{8} (x)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log_{8} (x^{\frac{1}{2}}) + \log_{8} (y)$

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

$\log_{8} (x^{\frac{1}{2}} y)$

Reorder factors in $\log_{8} (x^{\frac{1}{2}} y)$ .

$\log_{8} (y x^{\frac{1}{2}})$