Trigonometry Examples

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

Step 1

Rewrite $\log_{b} (\frac{x^{2} y^{4}}{y^{2}})$ as $\log_{b} (x^{2} y^{4}) - \log_{b} (y^{2})$ .

$\log_{b} (x^{2} y^{4}) - \log_{b} (y^{2})$

Step 2

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

$\log_{b} (x^{2} y^{4}) - (2 \log_{b} (y))$

Step 3

Multiply $2$ by $- 1$ .

$\log_{b} (x^{2} y^{4}) - 2 \log_{b} (y)$

Step 4

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

$\log_{b} (x^{2}) + \log_{b} (y^{4}) - 2 \log_{b} (y)$

Step 5

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

$2 \log_{b} (x) + \log_{b} (y^{4}) - 2 \log_{b} (y)$

Step 6

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

$2 \log_{b} (x) + 4 \log_{b} (y) - 2 \log_{b} (y)$

Step 7

Subtract $2 \log_{b} (y)$ from $4 \log_{b} (y)$ .

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