Expand the Logarithmic Expression log of (z^5x)/( square root of y^3)

$\log (\frac{z^{5} x}{\sqrt{y^{3}}})$

Step 1

Rewrite $\log (\frac{z^{5} x}{\sqrt{y^{3}}})$ as $\log (z^{5} x) - \log (\sqrt{y^{3}})$ .

$\log (z^{5} x) - \log (\sqrt{y^{3}})$

Step 2

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

$\log (z^{5} x) - \log (y^{\frac{3}{2}})$

Step 3

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

$\log (z^{5} x) - (\frac{3}{2} \log (y))$

Step 4

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

$\log (z^{5} x) - \frac{3 \log (y)}{2}$

Step 5

Rewrite $\log (z^{5} x)$ as $\log (z^{5}) + \log (x)$ .

$\log (z^{5}) + \log (x) - \frac{3 \log (y)}{2}$

Step 6

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

$5 \log (z) + \log (x) - \frac{3 \log (y)}{2}$