Algebra Examples

$\frac{\ln (24) + \ln (12)}{\log (24) + \log (12)}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{\ln (24 \cdot 12)}{\log (24) + \log (12)}$

Step 1.2

Multiply $24$ by $12$ .

$\frac{\ln (288)}{\log (24) + \log (12)}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{\ln (288)}{\log (24 \cdot 12)}$

Step 2.2

Multiply $24$ by $12$ .

$\frac{\ln (288)}{\log (288)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (288)}{\log (288)}$

Decimal Form:

$2.30258509 \dots$