Precalculus Examples

$\log_{4} (\frac{x^{6} y^{4}}{9})$

Step 1

Rewrite $\log_{4} (\frac{x^{6} y^{4}}{9})$ as $\log_{4} (x^{6} y^{4}) - \log_{4} (9)$ .

$\log_{4} (x^{6} y^{4}) - \log_{4} (9)$

Step 2

Rewrite $\log_{4} (9)$ as $\log_{4} (3^{2})$ .

$\log_{4} (x^{6} y^{4}) - \log_{4} (3^{2})$

Step 3

Expand $\log_{4} (3^{2})$ by moving $2$ outside the logarithm.

$\log_{4} (x^{6} y^{4}) - (2 \log_{4} (3))$

Step 4

Multiply $2$ by $- 1$ .

$\log_{4} (x^{6} y^{4}) - 2 \log_{4} (3)$

Step 5

Rewrite $\log_{4} (x^{6} y^{4})$ as $\log_{4} (x^{6}) + \log_{4} (y^{4})$ .

$\log_{4} (x^{6}) + \log_{4} (y^{4}) - 2 \log_{4} (3)$

Step 6

Expand $\log_{4} (x^{6})$ by moving $6$ outside the logarithm.

$6 \log_{4} (x) + \log_{4} (y^{4}) - 2 \log_{4} (3)$

Step 7

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

$6 \log_{4} (x) + 4 \log_{4} (y) - 2 \log_{4} (3)$