Finite Math Examples

$\frac{2 \ln (5) + \log (50)}{\log (4) - \ln (2)}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $\log (50)$ as $\log (2 \cdot 5^{2})$ .

$\frac{2 \ln (5) + \log (2 \cdot 5^{2})}{\log (4) - \ln (2)}$

Step 1.2

Rewrite $\log (2 \cdot 5^{2})$ as $\log (2) + \log (5^{2})$ .

$\frac{2 \ln (5) + \log (2) + \log (5^{2})}{\log (4) - \ln (2)}$

Step 1.3

Expand $\log (5^{2})$ by moving $2$ outside the logarithm.

$\frac{2 \ln (5) + \log (2) + 2 \log (5)}{\log (4) - \ln (2)}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $\log (4)$ as $\log (2^{2})$ .

$\frac{2 \ln (5) + \log (2) + 2 \log (5)}{\log (2^{2}) - \ln (2)}$

Step 2.2

Expand $\log (2^{2})$ by moving $2$ outside the logarithm.

$\frac{2 \ln (5) + \log (2) + 2 \log (5)}{2 \log (2) - \ln (2)}$