Precalculus Examples

$\log (100 x^{4} y^{6})$

Step 1

Rewrite $\log (100 x^{4} y^{6})$ as $\log (100 x^{4}) + \log (y^{6})$ .

$\log (100 x^{4}) + \log (y^{6})$

Step 2

Rewrite $\log (100 x^{4})$ as $\log (100) + \log (x^{4})$ .

$\log (100) + \log (x^{4}) + \log (y^{6})$

Step 3

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

$\log (100) + 4 \log (x) + \log (y^{6})$

Step 4

Expand $\log (y^{6})$ by moving $6$ outside the logarithm.

$\log (100) + 4 \log (x) + 6 \log (y)$

Step 5

Logarithm base $10$ of $100$ is $2$ .

$2 + 4 \log (x) + 6 \log (y)$