Precalculus Examples

$\frac{\ln (26) + \ln (13)}{\log (26) + \log (13)}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{\ln (26 \cdot 13)}{\log (26) + \log (13)}$

Step 1.2

Multiply $26$ by $13$ .

$\frac{\ln (338)}{\log (26) + \log (13)}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{\ln (338)}{\log (26 \cdot 13)}$

Step 2.2

Multiply $26$ by $13$ .

$\frac{\ln (338)}{\log (338)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (338)}{\log (338)}$

Decimal Form:

$2.30258509 \dots$