Precalculus Examples

$\log_{b} (\frac{7 x^{2}}{y^{4}})$

Step 1

Rewrite $\log_{b} (\frac{7 x^{2}}{y^{4}})$ as $\log_{b} (7 x^{2}) - \log_{b} (y^{4})$ .

$\log_{b} (7 x^{2}) - \log_{b} (y^{4})$

Step 2

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

$\log_{b} (7 x^{2}) - (4 \log_{b} (y))$

Step 3

Multiply $4$ by $- 1$ .

$\log_{b} (7 x^{2}) - 4 \log_{b} (y)$

Step 4

Rewrite $\log_{b} (7 x^{2})$ as $\log_{b} (7) + \log_{b} (x^{2})$ .

$\log_{b} (7) + \log_{b} (x^{2}) - 4 \log_{b} (y)$

Step 5

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

$\log_{b} (7) + 2 \log_{b} (x) - 4 \log_{b} (y)$