Basic Math Examples

$\ln (0.32) = - 0.00012 t$

Step 1

Rewrite the equation as $- 0.00012 t = \ln (0.32)$ .

$- 0.00012 t = \ln (0.32)$

Step 2

Divide each term in $- 0.00012 t = \ln (0.32)$ by $- 0.00012$ and simplify.

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Step 2.1

Divide each term in $- 0.00012 t = \ln (0.32)$ by $- 0.00012$ .

$\frac{- 0.00012 t}{- 0.00012} = \frac{\ln (0.32)}{- 0.00012}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 0.00012$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 0.00012 t}{- 0.00012} = \frac{\ln (0.32)}{- 0.00012}$

Step 2.2.1.2

Divide $t$ by $1$ .

$t = \frac{\ln (0.32)}{- 0.00012}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative in front of the fraction.

$t = - \frac{\ln (0.32)}{0.00012}$

Step 2.3.2

Replace $e$ with an approximation.

$t = - \frac{\log_{2.71828182} (0.32)}{0.00012}$

Step 2.3.3

Log base $2.71828182$ of $0.32$ is approximately $- 1.13943428$ .

$t = - \frac{- 1.13943428}{0.00012}$

Step 2.3.4

Divide $- 1.13943428$ by $0.00012$ .

$t = - - 9495.28569323$

Step 2.3.5

Multiply $- 1$ by $- 9495.28569323$ .

$t = 9495.28569323$