Precalculus Examples

$\frac{\ln (\frac{20}{71})}{\frac{1}{5} \cdot \ln (\frac{46}{71})}$

Step 1

Simplify $\frac{1}{5} \ln (\frac{46}{71})$ by moving $\frac{1}{5}$ inside the logarithm.

$\frac{\ln (\frac{20}{71})}{\ln ({(\frac{46}{71})}^{\frac{1}{5}})}$

Step 2

Apply the product rule to $\frac{46}{71}$ .

$\frac{\ln (\frac{20}{71})}{\ln (\frac{46^{\frac{1}{5}}}{71^{\frac{1}{5}}})}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (\frac{20}{71})}{\ln (\frac{46^{\frac{1}{5}}}{71^{\frac{1}{5}}})}$

Decimal Form:

$14.59487649 \dots$