Simplify/Condense 4 log base 16 of 12-4 log base 16 of 2

$4 \log_{16} (12) - 4 \log_{16} (2)$

Simplify $4 \log_{16} (12)$ by moving $4$ inside the logarithm.

$\log_{16} (12^{4}) - 4 \log_{16} (2)$

Raise $12$ to the power of $4$ .

$\log_{16} (20736) - 4 \log_{16} (2)$

Logarithm base $16$ of $2$ is $\frac{1}{4}$ .

$\log_{16} (20736) - 4 (\frac{1}{4})$

Cancel the common factor of $4$ .

Factor $4$ out of $- 4$ .

$\log_{16} (20736) + 4 (- 1) \frac{1}{4}$

Cancel the common factor.

$\log_{16} (20736) + 4 \cdot - 1 \frac{1}{4}$

Rewrite the expression.

$\log_{16} (20736) - 1$

The result can be shown in multiple forms.

Exact Form:

$\log_{16} (20736) - 1$

Decimal Form:

$2.58496250 \dots$