Precalculus Examples

$\log_{b} (x^{\frac{1}{2}} y^{3})$

Step 1

Rewrite $\log_{b} (x^{\frac{1}{2}} y^{3})$ as $\log_{b} (x^{\frac{1}{2}}) + \log_{b} (y^{3})$ .

$\log_{b} (x^{\frac{1}{2}}) + \log_{b} (y^{3})$

Step 2

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

$\frac{1}{2} \log_{b} (x) + \log_{b} (y^{3})$

Step 3

Expand $\log_{b} (y^{3})$ by moving $3$ outside the logarithm.

$\frac{1}{2} \log_{b} (x) + 3 \log_{b} (y)$

Step 4

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

$\frac{\log_{b} (x)}{2} + 3 \log_{b} (y)$