Finite Math Examples

$\ln (\frac{81000}{59871}) = 0.093 t$

Step 1

Rewrite the equation as $0.093 t = \ln (\frac{81000}{59871})$ .

$0.093 t = \ln (\frac{81000}{59871})$

Step 2

Reduce the expression $\frac{81000}{59871}$ by cancelling the common factors.

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Step 2.1

Factor $3$ out of $81000$ .

$0.093 t = \ln (\frac{3 (27000)}{59871})$

Step 2.2

Factor $3$ out of $59871$ .

$0.093 t = \ln (\frac{3 \cdot 27000}{3 \cdot 19957})$

Step 2.3

Cancel the common factor.

$0.093 t = \ln (\frac{3 \cdot 27000}{3 \cdot 19957})$

Step 2.4

Rewrite the expression.

$0.093 t = \ln (\frac{27000}{19957})$

Step 3

Divide each term in $0.093 t = \ln (\frac{27000}{19957})$ by $0.093$ and simplify.

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Step 3.1

Divide each term in $0.093 t = \ln (\frac{27000}{19957})$ by $0.093$ .

$\frac{0.093 t}{0.093} = \frac{\ln (\frac{27000}{19957})}{0.093}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $0.093$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{0.093 t}{0.093} = \frac{\ln (\frac{27000}{19957})}{0.093}$

Step 3.2.1.2

Divide $t$ by $1$ .

$t = \frac{\ln (\frac{27000}{19957})}{0.093}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Replace $e$ with an approximation.

$t = \frac{\log_{2.71828182} (\frac{27000}{19957})}{0.093}$

Step 3.3.2

Divide $27000$ by $19957$ .

$t = \frac{\log_{2.71828182} (1.35290875)}{0.093}$

Step 3.3.3

Log base $2.71828182$ of $1.35290875$ is approximately $0.3022569$ .

$t = \frac{0.3022569}{0.093}$

Step 3.3.4

Divide $0.3022569$ by $0.093$ .

$t = 3.25007426$