Finite Math Examples

$\frac{\ln (7900) - \ln (4000)}{0.045} = t$

Step 1

Rewrite the equation as $t = \frac{\ln (7900) - \ln (4000)}{0.045}$ .

$t = \frac{\ln (7900) - \ln (4000)}{0.045}$

Step 2

Simplify $\frac{\ln (7900) - \ln (4000)}{0.045}$ .

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Step 2.1

Simplify the numerator.

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Step 2.1.1

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

$t = \frac{\ln (\frac{7900}{4000})}{0.045}$

Step 2.1.2

Cancel the common factor of $7900$ and $4000$ .

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Step 2.1.2.1

Factor $100$ out of $7900$ .

$t = \frac{\ln (\frac{100 (79)}{4000})}{0.045}$

Step 2.1.2.2

Cancel the common factors.

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Step 2.1.2.2.1

Factor $100$ out of $4000$ .

$t = \frac{\ln (\frac{100 \cdot 79}{100 \cdot 40})}{0.045}$

Step 2.1.2.2.2

Cancel the common factor.

$t = \frac{\ln (\frac{100 \cdot 79}{100 \cdot 40})}{0.045}$

Step 2.1.2.2.3

Rewrite the expression.

$t = \frac{\ln (\frac{79}{40})}{0.045}$

Step 2.2

Replace $e$ with an approximation.

$t = \frac{\log_{2.71828182} (\frac{79}{40})}{0.045}$

Step 2.3

Divide $79$ by $40$ .

$t = \frac{\log_{2.71828182} (1.975)}{0.045}$

Step 2.4

Log base $2.71828182$ of $1.975$ is approximately $0.68056839$ .

$t = \frac{0.68056839}{0.045}$

Step 2.5

Divide $0.68056839$ by $0.045$ .

$t = 15.12374218$