Precalculus Examples

$\frac{\ln (100)}{100^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $\ln (100)$ as $\ln (2^{2} \cdot 5^{2})$ .

$\frac{\ln (2^{2} \cdot 5^{2})}{100^{2}}$

Step 1.2

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

$\frac{\ln (2^{2}) + \ln (5^{2})}{100^{2}}$

Step 1.3

Simplify each term.

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Step 1.3.1

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

$\frac{2 \ln (2) + \ln (5^{2})}{100^{2}}$

Step 1.3.2

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

$\frac{2 \ln (2) + 2 \ln (5)}{100^{2}}$

Step 1.4

Factor $2$ out of $2 \ln (2) + 2 \ln (5)$ .

$\frac{2 (\ln (2) + \ln (5))}{100^{2}}$

Step 2

Raise $100$ to the power of $2$ .

$\frac{2 (\ln (2) + \ln (5))}{10000}$

Step 3

Cancel the common factors.

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Step 3.1

Factor $2$ out of $10000$ .

$\frac{2 (\ln (2) + \ln (5))}{2 \cdot 5000}$

Step 3.2

Cancel the common factor.

$\frac{2 (\ln (2) + \ln (5))}{2 \cdot 5000}$

Step 3.3

Rewrite the expression.

$\frac{\ln (2) + \ln (5)}{5000}$