Precalculus Examples

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

Step 1

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

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

Step 2

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

$\log_{b} (x^{2}) + \log_{b} (y^{\frac{1}{2}})$

Step 3

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

$2 \log_{b} (x) + \log_{b} (y^{\frac{1}{2}})$

Step 4

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

$2 \log_{b} (x) + \frac{1}{2} \log_{b} (y)$

Step 5

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

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