Precalculus Examples

$\frac{\ln (2)}{12 \ln (\frac{1.105}{12})}$

Step 1

Rewrite $\ln (\frac{1.105}{12})$ as $\ln (1.105) - \ln (12)$ .

$\frac{\ln (2)}{12 (\ln (1.105) - \ln (12))}$

Step 2

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

$\frac{\ln (2)}{12 (\ln (1.105) - \ln (2^{2} \cdot 3))}$

Step 3

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

$\frac{\ln (2)}{12 (\ln (1.105) - (\ln (2^{2}) + \ln (3)))}$

Step 4

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

$\frac{\ln (2)}{12 (\ln (1.105) - (2 \ln (2) + \ln (3)))}$

Step 5

Apply the distributive property.

$\frac{\ln (2)}{12 (\ln (1.105) - (2 \ln (2)) - \ln (3))}$

Step 6

Multiply $2$ by $- 1$ .

$\frac{\ln (2)}{12 (\ln (1.105) - 2 \ln (2) - \ln (3))}$