Precalculus Examples

$\frac{\ln (5200) - \ln (3000)}{0.0375}$

Step 1

Simplify the numerator.

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Step 1.1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\frac{\ln (\frac{5200}{3000})}{0.0375}$

Step 1.2

Cancel the common factor of $5200$ and $3000$ .

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Step 1.2.1

Factor $200$ out of $5200$ .

$\frac{\ln (\frac{200 (26)}{3000})}{0.0375}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $200$ out of $3000$ .

$\frac{\ln (\frac{200 \cdot 26}{200 \cdot 15})}{0.0375}$

Step 1.2.2.2

Cancel the common factor.

$\frac{\ln (\frac{200 \cdot 26}{200 \cdot 15})}{0.0375}$

Step 1.2.2.3

Rewrite the expression.

$\frac{\ln (\frac{26}{15})}{0.0375}$

Step 2

Replace $e$ with an approximation.

$\frac{\log_{2.71828182} (\frac{26}{15})}{0.0375}$

Step 3

Divide $26$ by $15$ .

$\frac{\log_{2.71828182} (1.7\overline{3})}{0.0375}$

Step 4

Log base $2.71828182$ of $1.7\overline{3}$ is approximately $0.55004633$ .

$\frac{0.55004633}{0.0375}$

Step 5

Divide $0.55004633$ by $0.0375$ .

$14.66790231$