Precalculus Examples

$\log (100 x^{3} y^{5})$

Step 1

Rewrite $\log (100 x^{3} y^{5})$ as $\log (100 x^{3}) + \log (y^{5})$ .

$\log (100 x^{3}) + \log (y^{5})$

Step 2

Rewrite $\log (100 x^{3})$ as $\log (100) + \log (x^{3})$ .

$\log (100) + \log (x^{3}) + \log (y^{5})$

Step 3

Expand $\log (x^{3})$ by moving $3$ outside the logarithm.

$\log (100) + 3 \log (x) + \log (y^{5})$

Step 4

Expand $\log (y^{5})$ by moving $5$ outside the logarithm.

$\log (100) + 3 \log (x) + 5 \log (y)$

Step 5

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

$2 + 3 \log (x) + 5 \log (y)$