Precalculus Examples

$\frac{\ln (21) - \ln (19)}{2 \ln (19)}$

Step 1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\frac{\ln (\frac{21}{19})}{2 \ln (19)}$

Step 2

Simplify $2 \ln (19)$ by moving $2$ inside the logarithm.

$\frac{\ln (\frac{21}{19})}{\ln (19^{2})}$

Step 3

Raise $19$ to the power of $2$ .

$\frac{\ln (\frac{21}{19})}{\ln (361)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (\frac{21}{19})}{\ln (361)}$

Decimal Form:

$0.01699533 \dots$