Simplify/Condense log base 5 of 4+1/3 log base 5 of x

$\log_{5} (4) + \frac{1}{3} \log_{5} (x)$

Simplify $\frac{1}{3} \log_{5} (x)$ by moving $\frac{1}{3}$ inside the logarithm.

$\log_{5} (4) + \log_{5} (x^{\frac{1}{3}})$

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

$\log_{5} (4 x^{\frac{1}{3}})$