Expand the Logarithmic Expression log of (z square root of y^3)/x

$\log (\frac{z \sqrt{y^{3}}}{x})$

Rewrite $\log (\frac{z \sqrt{y^{3}}}{x})$ as $\log (z \sqrt{y^{3}}) - \log (x)$ .

$\log (z \sqrt{y^{3}}) - \log (x)$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y^{3}}$ as $y^{\frac{3}{2}}$ .

$\log (z y^{\frac{3}{2}}) - \log (x)$

Rewrite $\log (z y^{\frac{3}{2}})$ as $\log (z) + \log (y^{\frac{3}{2}})$ .

$\log (z) + \log (y^{\frac{3}{2}}) - \log (x)$

Expand $\log (y^{\frac{3}{2}})$ by moving $\frac{3}{2}$ outside the logarithm.

$\log (z) + \frac{3}{2} \log (y) - \log (x)$

Combine $\frac{3}{2}$ and $\log (y)$ .

$\log (z) + \frac{3 \log (y)}{2} - \log (x)$