Calculus Examples

$\ln (2) = 0.02 t$

Step 1

Rewrite the equation as $0.02 t = \ln (2)$ .

$0.02 t = \ln (2)$

Step 2

Divide each term in $0.02 t = \ln (2)$ by $0.02$ and simplify.

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Step 2.1

Divide each term in $0.02 t = \ln (2)$ by $0.02$ .

$\frac{0.02 t}{0.02} = \frac{\ln (2)}{0.02}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $0.02$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{0.02 t}{0.02} = \frac{\ln (2)}{0.02}$

Step 2.2.1.2

Divide $t$ by $1$ .

$t = \frac{\ln (2)}{0.02}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Replace $e$ with an approximation.

$t = \frac{\log_{2.71828182} (2)}{0.02}$

Step 2.3.2

Log base $2.71828182$ of $2$ is approximately $0.69314718$ .

$t = \frac{0.69314718}{0.02}$

Step 2.3.3

Divide $0.69314718$ by $0.02$ .

$t = 34.65735902$