Precalculus Examples

$\frac{2 \ln (3)}{\ln (4) - \ln (3)}$

Step 1

Simplify $2 \ln (3)$ by moving $2$ inside the logarithm.

$\frac{\ln (3^{2})}{\ln (4) - \ln (3)}$

Step 2

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

$\frac{\ln (3^{2})}{\ln (\frac{4}{3})}$

Step 3

Raise $3$ to the power of $2$ .

$\frac{\ln (9)}{\ln (\frac{4}{3})}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (9)}{\ln (\frac{4}{3})}$

Decimal Form:

$7.63768335 \dots$