Precalculus Examples

$\frac{12 \ln (2)}{\ln (\frac{22}{53})}$

Step 1

Simplify $12 \ln (2)$ by moving $12$ inside the logarithm.

$\frac{\ln (2^{12})}{\ln (\frac{22}{53})}$

Step 2

Raise $2$ to the power of $12$ .

$\frac{\ln (4096)}{\ln (\frac{22}{53})}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (4096)}{\ln (\frac{22}{53})}$

Decimal Form:

$- 9.46007537 \dots$