Evaluate ( natural log of 6+ natural log of 2)/( log of 6+ log of 2)

$\frac{\ln (6) + \ln (2)}{\log (6) + \log (2)}$

Simplify the numerator.

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\frac{\ln (6 \cdot 2)}{\log (6) + \log (2)}$

Multiply $6$ by $2$ .

$\frac{\ln (12)}{\log (6) + \log (2)}$

Simplify the denominator.

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\frac{\ln (12)}{\log (6 \cdot 2)}$

Multiply $6$ by $2$ .

$\frac{\ln (12)}{\log (12)}$

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (12)}{\log (12)}$

Decimal Form:

$2.30258509 \dots$