Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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

Step 6

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

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