Expand the Logarithmic Expression log of (x^2 square root of y^5)/z

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

Step 1

Rewrite $\log (\frac{x^{2} \sqrt{y^{5}}}{z})$ as $\log (x^{2} \sqrt{y^{5}}) - \log (z)$ .

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

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y^{5}}$ as $y^{\frac{5}{2}}$ .

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

Step 3

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

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

Step 4

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

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

Step 5

Expand $\log (y^{\frac{5}{2}})$ by moving $\frac{5}{2}$ outside the logarithm.

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

Step 6

Combine $\frac{5}{2}$ and $\log (y)$ .

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