Precalculus Examples

$\frac{\ln (\frac{3}{5})}{\frac{1}{15} \cdot \ln (\frac{11}{15})}$

Step 1

Simplify $\frac{1}{15} \ln (\frac{11}{15})$ by moving $\frac{1}{15}$ inside the logarithm.

$\frac{\ln (\frac{3}{5})}{\ln ({(\frac{11}{15})}^{\frac{1}{15}})}$

Step 2

Apply the product rule to $\frac{11}{15}$ .

$\frac{\ln (\frac{3}{5})}{\ln (\frac{11^{\frac{1}{15}}}{15^{\frac{1}{15}}})}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (\frac{3}{5})}{\ln (\frac{11^{\frac{1}{15}}}{15^{\frac{1}{15}}})}$

Decimal Form:

$24.70502209 \dots$