Precalculus Examples

$\log_{2} (x^{4} \sqrt{y^{5}})$

Step 1

Rewrite $\log_{2} (x^{4} \sqrt{y^{5}})$ as $\log_{2} (x^{4}) + \log_{2} (\sqrt{y^{5}})$ .

$\log_{2} (x^{4}) + \log_{2} (\sqrt{y^{5}})$

Step 2

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

$\log_{2} (x^{4}) + \log_{2} (y^{\frac{5}{2}})$

Step 3

Expand $\log_{2} (x^{4})$ by moving $4$ outside the logarithm.

$4 \log_{2} (x) + \log_{2} (y^{\frac{5}{2}})$

Step 4

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

$4 \log_{2} (x) + \frac{5}{2} \log_{2} (y)$

Step 5

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

$4 \log_{2} (x) + \frac{5 \log_{2} (y)}{2}$