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

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

Step 1

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

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

Step 2

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

$\log (x^{\frac{1}{2}} z) - \log (y^{3})$

Step 3

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

$\log (x^{\frac{1}{2}} z) - (3 \log (y))$

Step 4

Multiply $3$ by $- 1$ .

$\log (x^{\frac{1}{2}} z) - 3 \log (y)$

Step 5

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

$\log (x^{\frac{1}{2}}) + \log (z) - 3 \log (y)$

Step 6

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

$\frac{1}{2} \log (x) + \log (z) - 3 \log (y)$

Step 7

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

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