Precalculus Examples

$\log (\frac{m^{3} n}{\sqrt{y}})$

Step 1

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

$\log (m^{3} n) - \log (\sqrt{y})$

Step 2

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

$\log (m^{3} n) - \log (y^{\frac{1}{2}})$

Step 3

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

$\log (m^{3} n) - (\frac{1}{2} \log (y))$

Step 4

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

$\log (m^{3} n) - \frac{\log (y)}{2}$

Step 5

Rewrite $\log (m^{3} n)$ as $\log (m^{3}) + \log (n)$ .

$\log (m^{3}) + \log (n) - \frac{\log (y)}{2}$

Step 6

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

$3 \log (m) + \log (n) - \frac{\log (y)}{2}$