Simplify/Condense 1/3( log base 4 of x+ log base 4 of z)

$\frac{1}{3} (\log_{4} (x) + \log_{4} (z))$

Step 1

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

$\frac{1}{3} \cdot \log_{4} (x z)$

Step 2

Simplify $\frac{1}{3} \log_{4} (x z)$ by moving $\frac{1}{3}$ inside the logarithm.

$\log_{4} ({(x z)}^{\frac{1}{3}})$

Step 3

Apply the product rule to $x z$ .

$\log_{4} (x^{\frac{1}{3}} z^{\frac{1}{3}})$