Trigonometry Examples

$\frac{\ln (12) + \ln (4)}{\log (12) + \log (4)}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

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

$\frac{\ln (12 \cdot 4)}{\log (12) + \log (4)}$

Step 1.2

Multiply $12$ by $4$ .

$\frac{\ln (48)}{\log (12) + \log (4)}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

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

$\frac{\ln (48)}{\log (12 \cdot 4)}$

Step 2.2

Multiply $12$ by $4$ .

$\frac{\ln (48)}{\log (48)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (48)}{\log (48)}$

Decimal Form:

$2.30258509 \dots$