Finite Math Examples

$0.031 t = \ln (\frac{10000}{5500})$

Step 1

Reduce the expression $\frac{10000}{5500}$ by cancelling the common factors.

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Factor $500$ out of $10000$ .

$0.031 t = \ln (\frac{500 (20)}{5500})$

Factor $500$ out of $5500$ .

$0.031 t = \ln (\frac{500 \cdot 20}{500 \cdot 11})$

Cancel the common factor.

$0.031 t = \ln (\frac{500 \cdot 20}{500 \cdot 11})$

Rewrite the expression.

$0.031 t = \ln (\frac{20}{11})$

Step 2

Divide each term in $0.031 t = \ln (\frac{20}{11})$ by $0.031$ and simplify.

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Divide each term in $0.031 t = \ln (\frac{20}{11})$ by $0.031$ .

$\frac{0.031 t}{0.031} = \frac{\ln (\frac{20}{11})}{0.031}$

Simplify the left side.

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Cancel the common factor of $0.031$ .

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Cancel the common factor.

$\frac{0.031 t}{0.031} = \frac{\ln (\frac{20}{11})}{0.031}$

Divide $t$ by $1$ .

$t = \frac{\ln (\frac{20}{11})}{0.031}$

Simplify the right side.

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Replace $e$ with an approximation.

$t = \frac{\log_{2.71828182} (\frac{20}{11})}{0.031}$

Divide $20$ by $11$ .

$t = \frac{\log_{2.71828182} (1.\overline{81})}{0.031}$

Log base $2.71828182$ of $1.\overline{81}$ is approximately $0.597837$ .

$t = \frac{0.597837}{0.031}$

Divide $0.597837$ by $0.031$ .

$t = 19.28506454$