Precalculus Examples

$12^{2 (- \frac{\ln (11)}{\ln (12)})}$

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

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

$12^{2 (- \frac{\ln (11)}{\ln (2^{2} \cdot 3)})}$

Step 1.2

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

$12^{2 (- \frac{\ln (11)}{\ln (2^{2}) + \ln (3)})}$

Step 1.3

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

$12^{2 (- \frac{\ln (11)}{2 \ln (2) + \ln (3)})}$

Step 2

Multiply $2 (- \frac{\ln (11)}{2 \ln (2) + \ln (3)})$ .

Tap for more steps...

Step 2.1

Multiply $- 1$ by $2$ .

$12^{- 2 \frac{\ln (11)}{2 \ln (2) + \ln (3)}}$

Step 2.2

Combine $- 2$ and $\frac{\ln (11)}{2 \ln (2) + \ln (3)}$ .

$12^{\frac{- 2 \ln (11)}{2 \ln (2) + \ln (3)}}$

Step 3

Move the negative in front of the fraction.

$12^{- \frac{2 \ln (11)}{2 \ln (2) + \ln (3)}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$12^{- \frac{2 \ln (11)}{2 \ln (2) + \ln (3)}}$

Decimal Form:

$0.00826446 \dots$