Precalculus Examples

$\log (10000 x^{2} y^{4})$

Step 1

Rewrite $\log (10000 x^{2} y^{4})$ as $\log (10000 x^{2}) + \log (y^{4})$ .

$\log (10000 x^{2}) + \log (y^{4})$

Step 2

Rewrite $\log (10000 x^{2})$ as $\log (10000) + \log (x^{2})$ .

$\log (10000) + \log (x^{2}) + \log (y^{4})$

Step 3

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

$\log (10000) + 2 \log (x) + \log (y^{4})$

Step 4

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

$\log (10000) + 2 \log (x) + 4 \log (y)$

Step 5

Logarithm base $10$ of $10000$ is $4$ .

$4 + 2 \log (x) + 4 \log (y)$