How do you simplify this logarithm?

Question

$$\large\log\sqrt[3]{\frac{x^2y^5}{z}}$$

I think this is the answer, but I'm not positive:$$\frac{1}{3}\left((2\log{x}+5\log{y})-(\log{z})\right)$$

Answer 1

You are correct. In general, your subtracting for division and fraction for cube root is sound.