Finite Math Examples

$\frac{\ln (11800) - \ln (6000)}{0.0275} = t$

Step 1

Rewrite the equation as $t = \frac{\ln (11800) - \ln (6000)}{0.0275}$ .

$t = \frac{\ln (11800) - \ln (6000)}{0.0275}$

Step 2

Simplify $\frac{\ln (11800) - \ln (6000)}{0.0275}$ .

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Step 2.1

Simplify the numerator.

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Step 2.1.1

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

$t = \frac{\ln (\frac{11800}{6000})}{0.0275}$

Step 2.1.2

Cancel the common factor of $11800$ and $6000$ .

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Step 2.1.2.1

Factor $200$ out of $11800$ .

$t = \frac{\ln (\frac{200 (59)}{6000})}{0.0275}$

Step 2.1.2.2

Cancel the common factors.

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Step 2.1.2.2.1

Factor $200$ out of $6000$ .

$t = \frac{\ln (\frac{200 \cdot 59}{200 \cdot 30})}{0.0275}$

Step 2.1.2.2.2

Cancel the common factor.

$t = \frac{\ln (\frac{200 \cdot 59}{200 \cdot 30})}{0.0275}$

Step 2.1.2.2.3

Rewrite the expression.

$t = \frac{\ln (\frac{59}{30})}{0.0275}$

Step 2.2

Replace $e$ with an approximation.

$t = \frac{\log_{2.71828182} (\frac{59}{30})}{0.0275}$

Step 2.3

Divide $59$ by $30$ .

$t = \frac{\log_{2.71828182} (1.9\overline{6})}{0.0275}$

Step 2.4

Log base $2.71828182$ of $1.9\overline{6}$ is approximately $0.67634006$ .

$t = \frac{0.67634006}{0.0275}$

Step 2.5

Divide $0.67634006$ by $0.0275$ .

$t = 24.59418408$