Precalculus Examples

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

Step 1

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

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

Step 2

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

$2 \log_{b} (x) - \log_{b} (2 y)$

Step 3

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

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

Step 4

Apply the distributive property.

$2 \log_{b} (x) - \log_{b} (2) - \log_{b} (y)$