Precalculus Examples

$\frac{\ln (\frac{7}{27})}{\ln (\frac{7}{3})}$

Step 1

Rewrite $\ln (\frac{7}{27})$ as $\ln (7) - \ln (27)$ .

$\frac{\ln (7) - \ln (27)}{\ln (\frac{7}{3})}$

Step 2

Rewrite $\ln (27)$ as $\ln (3^{3})$ .

$\frac{\ln (7) - \ln (3^{3})}{\ln (\frac{7}{3})}$

Step 3

Expand $\ln (3^{3})$ by moving $3$ outside the logarithm.

$\frac{\ln (7) - (3 \ln (3))}{\ln (\frac{7}{3})}$

Step 4

Multiply $3$ by $- 1$ .

$\frac{\ln (7) - 3 \ln (3)}{\ln (\frac{7}{3})}$

Step 5

Rewrite $\ln (\frac{7}{3})$ as $\ln (7) - \ln (3)$ .

$\frac{\ln (7) - 3 \ln (3)}{\ln (7) - \ln (3)}$