Precalculus Examples

$\log ({(12)}^{1048576})$

Step 1

Expand $\log ({(12)}^{1048576})$ by moving $1048576$ outside the logarithm.

$1048576 \log (12)$

Step 2

Rewrite $\log (12)$ as $\log (2^{2} \cdot 3)$ .

$1048576 \log (2^{2} \cdot 3)$

Step 3

Rewrite $\log (2^{2} \cdot 3)$ as $\log (2^{2}) + \log (3)$ .

$1048576 (\log (2^{2}) + \log (3))$

Step 4

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

$1048576 (2 \log (2) + \log (3))$

Step 5

Apply the distributive property.

$1048576 (2 \log (2)) + 1048576 \log (3)$

Step 6

Multiply $2$ by $1048576$ .

$2097152 \log (2) + 1048576 \log (3)$