Precalculus Examples

$\frac{\ln (\frac{0.1}{0.3})}{\frac{\ln (\frac{0.27}{0.3})}{30}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\ln (\frac{0.1}{0.3}) \frac{30}{\ln (\frac{0.27}{0.3})}$

Step 2

Divide $0.1$ by $0.3$ .

$\ln (0.\overline{3}) \frac{30}{\ln (\frac{0.27}{0.3})}$

Step 3

Divide $0.27$ by $0.3$ .

$\ln (0.\overline{3}) \frac{30}{\ln (0.9)}$

Step 4

Multiply $\ln (0.\overline{3}) \frac{30}{\ln (0.9)}$ .

Tap for more steps...

Step 4.1

Combine $\ln (0.\overline{3})$ and $\frac{30}{\ln (0.9)}$ .

$\frac{\ln (0.\overline{3}) \cdot 30}{\ln (0.9)}$

Step 4.2

Reorder $\ln (0.\overline{3})$ and $30$ .

$\frac{30 \cdot \ln (0.\overline{3})}{\ln (0.9)}$

Step 4.3

Simplify $30 \cdot \ln (0.\overline{3})$ by moving $30$ inside the logarithm.

$\frac{\ln ({0.\overline{3}}^{30})}{\ln (0.9)}$

Step 5

Raise $0.\overline{3}$ to the power of $30$ .

$\frac{\ln (0)}{\ln (0.9)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (0)}{\ln (0.9)}$

Decimal Form:

$312.81517990 \dots$