Precalculus Examples

$\frac{\log (15) + \log (20)}{\ln (15) + \ln (20)}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{\log (15 \cdot 20)}{\ln (15) + \ln (20)}$

Step 1.2

Multiply $15$ by $20$ .

$\frac{\log (300)}{\ln (15) + \ln (20)}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{\log (300)}{\ln (15 \cdot 20)}$

Step 2.2

Multiply $15$ by $20$ .

$\frac{\log (300)}{\ln (300)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (300)}{\ln (300)}$

Decimal Form:

$0.43429448 \dots$