# How do you solve (1/4) e^(-2 t) = 0.1?

$t = 0.458145$

#### Explanation:

Start from the given equation

$\left(\frac{1}{4}\right) \cdot {e}^{- 2 t} = 0.1$

$4 \cdot \left(\frac{1}{4}\right) \cdot {e}^{- 2 t} = 4 \left(0.1\right)$ Multiply both sides by $4$

${e}^{- 2 t} = 0.4$

$\ln {e}^{- 2 t} = \ln 0.4$ Take the logarithm of both sides

$- 2 t = \ln 0.4$

$\frac{- 2 t}{-} 2 = \frac{\ln 0.4}{-} 2$ Divide both sides by $- 2$

$\frac{\cancel{- 2} t}{\cancel{- 2}} = \frac{\ln 0.4}{-} 2$

$t = \frac{\ln 0.4}{-} 2$

$t = 0.458145$

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