Expand the Logarithmic Expression log of (y^5 square root of x)/z

$\log (\frac{y^{5} \sqrt{x}}{z})$

Rewrite $\log (\frac{y^{5} \sqrt{x}}{z})$ as $\log (y^{5} \sqrt{x}) - \log (z)$ .

$\log (y^{5} \sqrt{x}) - \log (z)$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$\log (y^{5} x^{\frac{1}{2}}) - \log (z)$

Rewrite $\log (y^{5} x^{\frac{1}{2}})$ as $\log (y^{5}) + \log (x^{\frac{1}{2}})$ .

$\log (y^{5}) + \log (x^{\frac{1}{2}}) - \log (z)$

Expand $\log (y^{5})$ by moving $5$ outside the logarithm.

$5 \log (y) + \log (x^{\frac{1}{2}}) - \log (z)$

Expand $\log (x^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$5 \log (y) + \frac{1}{2} \log (x) - \log (z)$

Combine $\frac{1}{2}$ and $\log (x)$ .

$5 \log (y) + \frac{\log (x)}{2} - \log (z)$