Precalculus Examples

$\log_{a} (8 x^{2} y)$

Step 1

Rewrite $\log_{a} (8 x^{2} y)$ as $\log_{a} (8 x^{2}) + \log_{a} (y)$ .

$\log_{a} (8 x^{2}) + \log_{a} (y)$

Step 2

Rewrite $\log_{a} (8 x^{2})$ as $\log_{a} (8) + \log_{a} (x^{2})$ .

$\log_{a} (8) + \log_{a} (x^{2}) + \log_{a} (y)$

Step 3

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

$\log_{a} (8) + 2 \log_{a} (x) + \log_{a} (y)$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Rewrite $\log_{a} (8)$ as $\log_{a} (2^{3})$ .

$\log_{a} (2^{3}) + 2 \log_{a} (x) + \log_{a} (y)$

Step 4.2

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

$3 \log_{a} (2) + 2 \log_{a} (x) + \log_{a} (y)$