Basic Math Examples

$0.32 = - 14 e^{- 0.000121 t}$

Step 1

Rewrite the equation as $- 14 e^{- 0.000121 t} = 0.32$ .

$- 14 e^{- 0.000121 t} = 0.32$

Step 2

Divide each term in $- 14 e^{- 0.000121 t} = 0.32$ by $- 14$ and simplify.

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Step 2.1

Divide each term in $- 14 e^{- 0.000121 t} = 0.32$ by $- 14$ .

$\frac{- 14 e^{- 0.000121 t}}{- 14} = \frac{0.32}{- 14}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 14$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 14 e^{- 0.000121 t}}{- 14} = \frac{0.32}{- 14}$

Step 2.2.1.2

Divide $e^{- 0.000121 t}$ by $1$ .

$e^{- 0.000121 t} = \frac{0.32}{- 14}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0.32$ by $- 14$ .

$e^{- 0.000121 t} = - 0.02285714$

Step 3

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (e^{- 0.000121 t}) = \ln (- 0.02285714)$

Step 4

The equation cannot be solved because $\ln (- 0.02285714)$ is undefined.

Undefined

Step 5

There is no solution for $e^{- 0.000121 t} = - 0.02285714$

No solution